Struct Complex

#[repr(C)]
pub struct Complex<T> {
    pub re: T,
    pub im: T,
}

A complex number in Cartesian form.

Representation and Foreign Function Interface Compatibility

Complex<T> is memory layout compatible with an array [T; 2].

Note that Complex<F> where F is a floating point type is only memory layout compatible with C’s complex types, not necessarily calling convention compatible. This means that for FFI you can only pass Complex<F> behind a pointer, not as a value.

Examples

Example of extern function declaration.

use num_complex::Complex;
use std::os::raw::c_int;

extern "C" {
    fn zaxpy_(n: *const c_int, alpha: *const Complex<f64>,
              x: *const Complex<f64>, incx: *const c_int,
              y: *mut Complex<f64>, incy: *const c_int);
}

Fields

re: T

Real portion of the complex number

im: T

Imaginary portion of the complex number

Implementations

impl<T> Complex<T>

pub const fn new(re: T, im: T) -> Self

Create a new Complex

impl<T: Clone + Num> Complex<T>

pub fn i() -> Self

Returns imaginary unit

pub fn norm_sqr(&self) -> T

Returns the square of the norm (since T doesn’t necessarily have a sqrt function), i.e. re^2 + im^2.

pub fn scale(&self, t: T) -> Self

Multiplies self by the scalar t.

pub fn unscale(&self, t: T) -> Self

Divides self by the scalar t.

pub fn powu(&self, exp: u32) -> Self

Raises self to an unsigned integer power.

impl<T: Clone + Num + Neg<Output = T>> Complex<T>

pub fn conj(&self) -> Self

Returns the complex conjugate. i.e. re - i im

pub fn inv(&self) -> Self

Returns 1/self

pub fn powi(&self, exp: i32) -> Self

Raises self to a signed integer power.

impl<T: Clone + Signed> Complex<T>

pub fn l1_norm(&self) -> T

Returns the L1 norm |re| + |im| – the Manhattan distance from the origin.

impl<T: Float> Complex<T>

pub fn norm(self) -> T

Calculate |self|

pub fn arg(self) -> T

Calculate the principal Arg of self.

pub fn to_polar(self) -> (T, T)

Convert to polar form (r, theta), such that self = r * exp(i * theta)

pub fn from_polar(r: T, theta: T) -> Self

Convert a polar representation into a complex number.

pub fn exp(self) -> Self

Computes e^(self), where e is the base of the natural logarithm.

pub fn ln(self) -> Self

Computes the principal value of natural logarithm of self.

This function has one branch cut:

• (-∞, 0], continuous from above.

The branch satisfies -π ≤ arg(ln(z)) ≤ π.

pub fn sqrt(self) -> Self

Computes the principal value of the square root of self.

This function has one branch cut:

• (-∞, 0), continuous from above.

The branch satisfies -π/2 ≤ arg(sqrt(z)) ≤ π/2.

pub fn cbrt(self) -> Self

Computes the principal value of the cube root of self.

This function has one branch cut:

• (-∞, 0), continuous from above.

The branch satisfies -π/3 ≤ arg(cbrt(z)) ≤ π/3.

Note that this does not match the usual result for the cube root of negative real numbers. For example, the real cube root of -8 is -2, but the principal complex cube root of -8 is 1 + i√3.

pub fn powf(self, exp: T) -> Self

Raises self to a floating point power.

pub fn log(self, base: T) -> Self

Returns the logarithm of self with respect to an arbitrary base.

pub fn powc(self, exp: Self) -> Self

Raises self to a complex power.

pub fn expf(self, base: T) -> Self

Raises a floating point number to the complex power self.

pub fn sin(self) -> Self

Computes the sine of self.

pub fn cos(self) -> Self

Computes the cosine of self.

pub fn tan(self) -> Self

Computes the tangent of self.

pub fn asin(self) -> Self

Computes the principal value of the inverse sine of self.

This function has two branch cuts:

• (-∞, -1), continuous from above.
• (1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Re(asin(z)) ≤ π/2.

pub fn acos(self) -> Self

Computes the principal value of the inverse cosine of self.

This function has two branch cuts:

• (-∞, -1), continuous from above.
• (1, ∞), continuous from below.

The branch satisfies 0 ≤ Re(acos(z)) ≤ π.

pub fn atan(self) -> Self

Computes the principal value of the inverse tangent of self.

This function has two branch cuts:

• (-∞i, -i], continuous from the left.
• [i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Re(atan(z)) ≤ π/2.

pub fn sinh(self) -> Self

Computes the hyperbolic sine of self.

pub fn cosh(self) -> Self

Computes the hyperbolic cosine of self.

pub fn tanh(self) -> Self

Computes the hyperbolic tangent of self.

pub fn asinh(self) -> Self

Computes the principal value of inverse hyperbolic sine of self.

This function has two branch cuts:

• (-∞i, -i), continuous from the left.
• (i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Im(asinh(z)) ≤ π/2.

pub fn acosh(self) -> Self

Computes the principal value of inverse hyperbolic cosine of self.

This function has one branch cut:

• (-∞, 1), continuous from above.

The branch satisfies -π ≤ Im(acosh(z)) ≤ π and 0 ≤ Re(acosh(z)) < ∞.

pub fn atanh(self) -> Self

Computes the principal value of inverse hyperbolic tangent of self.

This function has two branch cuts:

• (-∞, -1], continuous from above.
• [1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Im(atanh(z)) ≤ π/2.

pub fn finv(self) -> Complex<T>

Returns 1/self using floating-point operations.

This may be more accurate than the generic self.inv() in cases where self.norm_sqr() would overflow to ∞ or underflow to 0.

Examples

use num_complex::Complex64;
let c = Complex64::new(1e300, 1e300);

// The generic `inv()` will overflow.
assert!(!c.inv().is_normal());

// But we can do better for `Float` types.
let inv = c.finv();
assert!(inv.is_normal());
println!("{:e}", inv);

let expected = Complex64::new(5e-301, -5e-301);
assert!((inv - expected).norm() < 1e-315);

pub fn fdiv(self, other: Complex<T>) -> Complex<T>

Returns self/other using floating-point operations.

This may be more accurate than the generic Div implementation in cases where other.norm_sqr() would overflow to ∞ or underflow to 0.

Examples

use num_complex::Complex64;
let a = Complex64::new(2.0, 3.0);
let b = Complex64::new(1e300, 1e300);

// Generic division will overflow.
assert!(!(a / b).is_normal());

// But we can do better for `Float` types.
let quotient = a.fdiv(b);
assert!(quotient.is_normal());
println!("{:e}", quotient);

let expected = Complex64::new(2.5e-300, 5e-301);
assert!((quotient - expected).norm() < 1e-315);

impl<T: FloatCore> Complex<T>

pub fn is_nan(self) -> bool

Checks if the given complex number is NaN

pub fn is_infinite(self) -> bool

Checks if the given complex number is infinite

pub fn is_finite(self) -> bool

Checks if the given complex number is finite

pub fn is_normal(self) -> bool

Checks if the given complex number is normal

Trait Implementations

impl<'a, 'b, T: Clone + Num> Add<&'b Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the + operator.

fn add(self, other: &Complex<T>) -> Self::Output

Performs the + operation.

impl<'a, T: Clone + Num> Add<&'a Complex<T>> for Complex<T>

type Output = Complex<T>

The resulting type after applying the + operator.

fn add(self, other: &Complex<T>) -> Self::Output

Performs the + operation.

impl<'a, 'b> Add<&'a Complex<f32>> for &'b f32

type Output = Complex<f32>

The resulting type after applying the + operator.

fn add(self, other: &Complex<f32>) -> Complex<f32>

Performs the + operation.

impl<'a> Add<&'a Complex<f32>> for f32

type Output = Complex<f32>

The resulting type after applying the + operator.

fn add(self, other: &Complex<f32>) -> Complex<f32>

Performs the + operation.

impl<'a, 'b> Add<&'a Complex<f64>> for &'b f64

type Output = Complex<f64>

The resulting type after applying the + operator.

fn add(self, other: &Complex<f64>) -> Complex<f64>

Performs the + operation.

impl<'a> Add<&'a Complex<f64>> for f64

type Output = Complex<f64>

The resulting type after applying the + operator.

fn add(self, other: &Complex<f64>) -> Complex<f64>

Performs the + operation.

impl<'a, 'b> Add<&'a Complex<i128>> for &'b i128

type Output = Complex<i128>

The resulting type after applying the + operator.

fn add(self, other: &Complex<i128>) -> Complex<i128>

Performs the + operation.

impl<'a> Add<&'a Complex<i128>> for i128

type Output = Complex<i128>

The resulting type after applying the + operator.

fn add(self, other: &Complex<i128>) -> Complex<i128>

Performs the + operation.

impl<'a, 'b> Add<&'a Complex<i16>> for &'b i16

type Output = Complex<i16>

The resulting type after applying the + operator.

fn add(self, other: &Complex<i16>) -> Complex<i16>

Performs the + operation.

impl<'a> Add<&'a Complex<i16>> for i16

type Output = Complex<i16>

The resulting type after applying the + operator.

fn add(self, other: &Complex<i16>) -> Complex<i16>

Performs the + operation.

impl<'a, 'b> Add<&'a Complex<i32>> for &'b i32

type Output = Complex<i32>

The resulting type after applying the + operator.

fn add(self, other: &Complex<i32>) -> Complex<i32>

Performs the + operation.

impl<'a> Add<&'a Complex<i32>> for i32

type Output = Complex<i32>

The resulting type after applying the + operator.

fn add(self, other: &Complex<i32>) -> Complex<i32>

Performs the + operation.

impl<'a, 'b> Add<&'a Complex<i64>> for &'b i64

type Output = Complex<i64>

The resulting type after applying the + operator.

fn add(self, other: &Complex<i64>) -> Complex<i64>

Performs the + operation.

impl<'a> Add<&'a Complex<i64>> for i64

type Output = Complex<i64>

The resulting type after applying the + operator.

fn add(self, other: &Complex<i64>) -> Complex<i64>

Performs the + operation.

impl<'a, 'b> Add<&'a Complex<i8>> for &'b i8

type Output = Complex<i8>

The resulting type after applying the + operator.

fn add(self, other: &Complex<i8>) -> Complex<i8>

Performs the + operation.

impl<'a> Add<&'a Complex<i8>> for i8

type Output = Complex<i8>

The resulting type after applying the + operator.

fn add(self, other: &Complex<i8>) -> Complex<i8>

Performs the + operation.

impl<'a, 'b> Add<&'a Complex<isize>> for &'b isize

type Output = Complex<isize>

The resulting type after applying the + operator.

fn add(self, other: &Complex<isize>) -> Complex<isize>

Performs the + operation.

impl<'a> Add<&'a Complex<isize>> for isize

type Output = Complex<isize>

The resulting type after applying the + operator.

fn add(self, other: &Complex<isize>) -> Complex<isize>

Performs the + operation.

impl<'a, 'b> Add<&'a Complex<u128>> for &'b u128

type Output = Complex<u128>

The resulting type after applying the + operator.

fn add(self, other: &Complex<u128>) -> Complex<u128>

Performs the + operation.

impl<'a> Add<&'a Complex<u128>> for u128

type Output = Complex<u128>

The resulting type after applying the + operator.

fn add(self, other: &Complex<u128>) -> Complex<u128>

Performs the + operation.

impl<'a, 'b> Add<&'a Complex<u16>> for &'b u16

type Output = Complex<u16>

The resulting type after applying the + operator.

fn add(self, other: &Complex<u16>) -> Complex<u16>

Performs the + operation.

impl<'a> Add<&'a Complex<u16>> for u16

type Output = Complex<u16>

The resulting type after applying the + operator.

fn add(self, other: &Complex<u16>) -> Complex<u16>

Performs the + operation.

impl<'a, 'b> Add<&'a Complex<u32>> for &'b u32

type Output = Complex<u32>

The resulting type after applying the + operator.

fn add(self, other: &Complex<u32>) -> Complex<u32>

Performs the + operation.

impl<'a> Add<&'a Complex<u32>> for u32

type Output = Complex<u32>

The resulting type after applying the + operator.

fn add(self, other: &Complex<u32>) -> Complex<u32>

Performs the + operation.

impl<'a, 'b> Add<&'a Complex<u64>> for &'b u64

type Output = Complex<u64>

The resulting type after applying the + operator.

fn add(self, other: &Complex<u64>) -> Complex<u64>

Performs the + operation.

impl<'a> Add<&'a Complex<u64>> for u64

type Output = Complex<u64>

The resulting type after applying the + operator.

fn add(self, other: &Complex<u64>) -> Complex<u64>

Performs the + operation.

impl<'a, 'b> Add<&'a Complex<u8>> for &'b u8

type Output = Complex<u8>

The resulting type after applying the + operator.

fn add(self, other: &Complex<u8>) -> Complex<u8>

Performs the + operation.

impl<'a> Add<&'a Complex<u8>> for u8

type Output = Complex<u8>

The resulting type after applying the + operator.

fn add(self, other: &Complex<u8>) -> Complex<u8>

Performs the + operation.

impl<'a, 'b> Add<&'a Complex<usize>> for &'b usize

type Output = Complex<usize>

The resulting type after applying the + operator.

fn add(self, other: &Complex<usize>) -> Complex<usize>

Performs the + operation.

impl<'a> Add<&'a Complex<usize>> for usize

type Output = Complex<usize>

The resulting type after applying the + operator.

fn add(self, other: &Complex<usize>) -> Complex<usize>

Performs the + operation.

impl<'a, 'b, T: Clone + Num> Add<&'a T> for &'b Complex<T>

type Output = Complex<T>

The resulting type after applying the + operator.

fn add(self, other: &T) -> Self::Output

Performs the + operation.

impl<'a, T: Clone + Num> Add<&'a T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the + operator.

fn add(self, other: &T) -> Self::Output

Performs the + operation.

impl<'a, T: Clone + Num> Add<Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the + operator.

fn add(self, other: Complex<T>) -> Self::Output

Performs the + operation.

impl<'a> Add<Complex<f32>> for &'a f32

type Output = Complex<f32>

The resulting type after applying the + operator.

fn add(self, other: Complex<f32>) -> Complex<f32>

Performs the + operation.

impl Add<Complex<f32>> for f32

type Output = Complex<f32>

The resulting type after applying the + operator.

fn add(self, other: Complex<f32>) -> Self::Output

Performs the + operation.

impl<'a> Add<Complex<f64>> for &'a f64

type Output = Complex<f64>

The resulting type after applying the + operator.

fn add(self, other: Complex<f64>) -> Complex<f64>

Performs the + operation.

impl Add<Complex<f64>> for f64

type Output = Complex<f64>

The resulting type after applying the + operator.

fn add(self, other: Complex<f64>) -> Self::Output

Performs the + operation.

impl<'a> Add<Complex<i128>> for &'a i128

type Output = Complex<i128>

The resulting type after applying the + operator.

fn add(self, other: Complex<i128>) -> Complex<i128>

Performs the + operation.

impl Add<Complex<i128>> for i128

type Output = Complex<i128>

The resulting type after applying the + operator.

fn add(self, other: Complex<i128>) -> Self::Output

Performs the + operation.

impl<'a> Add<Complex<i16>> for &'a i16

type Output = Complex<i16>

The resulting type after applying the + operator.

fn add(self, other: Complex<i16>) -> Complex<i16>

Performs the + operation.

impl Add<Complex<i16>> for i16

type Output = Complex<i16>

The resulting type after applying the + operator.

fn add(self, other: Complex<i16>) -> Self::Output

Performs the + operation.

impl<'a> Add<Complex<i32>> for &'a i32

type Output = Complex<i32>

The resulting type after applying the + operator.

fn add(self, other: Complex<i32>) -> Complex<i32>

Performs the + operation.

impl Add<Complex<i32>> for i32

type Output = Complex<i32>

The resulting type after applying the + operator.

fn add(self, other: Complex<i32>) -> Self::Output

Performs the + operation.

impl<'a> Add<Complex<i64>> for &'a i64

type Output = Complex<i64>

The resulting type after applying the + operator.

fn add(self, other: Complex<i64>) -> Complex<i64>

Performs the + operation.

impl Add<Complex<i64>> for i64

type Output = Complex<i64>

The resulting type after applying the + operator.

fn add(self, other: Complex<i64>) -> Self::Output

Performs the + operation.

impl<'a> Add<Complex<i8>> for &'a i8

type Output = Complex<i8>

The resulting type after applying the + operator.

fn add(self, other: Complex<i8>) -> Complex<i8>

Performs the + operation.

impl Add<Complex<i8>> for i8

type Output = Complex<i8>

The resulting type after applying the + operator.

fn add(self, other: Complex<i8>) -> Self::Output

Performs the + operation.

impl<'a> Add<Complex<isize>> for &'a isize

type Output = Complex<isize>

The resulting type after applying the + operator.

fn add(self, other: Complex<isize>) -> Complex<isize>

Performs the + operation.

impl Add<Complex<isize>> for isize

type Output = Complex<isize>

The resulting type after applying the + operator.

fn add(self, other: Complex<isize>) -> Self::Output

Performs the + operation.

impl<'a> Add<Complex<u128>> for &'a u128

type Output = Complex<u128>

The resulting type after applying the + operator.

fn add(self, other: Complex<u128>) -> Complex<u128>

Performs the + operation.

impl Add<Complex<u128>> for u128

type Output = Complex<u128>

The resulting type after applying the + operator.

fn add(self, other: Complex<u128>) -> Self::Output

Performs the + operation.

impl<'a> Add<Complex<u16>> for &'a u16

type Output = Complex<u16>

The resulting type after applying the + operator.

fn add(self, other: Complex<u16>) -> Complex<u16>

Performs the + operation.

impl Add<Complex<u16>> for u16

type Output = Complex<u16>

The resulting type after applying the + operator.

fn add(self, other: Complex<u16>) -> Self::Output

Performs the + operation.

impl<'a> Add<Complex<u32>> for &'a u32

type Output = Complex<u32>

The resulting type after applying the + operator.

fn add(self, other: Complex<u32>) -> Complex<u32>

Performs the + operation.

impl Add<Complex<u32>> for u32

type Output = Complex<u32>

The resulting type after applying the + operator.

fn add(self, other: Complex<u32>) -> Self::Output

Performs the + operation.

impl<'a> Add<Complex<u64>> for &'a u64

type Output = Complex<u64>

The resulting type after applying the + operator.

fn add(self, other: Complex<u64>) -> Complex<u64>

Performs the + operation.

impl Add<Complex<u64>> for u64

type Output = Complex<u64>

The resulting type after applying the + operator.

fn add(self, other: Complex<u64>) -> Self::Output

Performs the + operation.

impl<'a> Add<Complex<u8>> for &'a u8

type Output = Complex<u8>

The resulting type after applying the + operator.

fn add(self, other: Complex<u8>) -> Complex<u8>

Performs the + operation.

impl Add<Complex<u8>> for u8

type Output = Complex<u8>

The resulting type after applying the + operator.

fn add(self, other: Complex<u8>) -> Self::Output

Performs the + operation.

impl<'a> Add<Complex<usize>> for &'a usize

type Output = Complex<usize>

The resulting type after applying the + operator.

fn add(self, other: Complex<usize>) -> Complex<usize>

Performs the + operation.

impl Add<Complex<usize>> for usize

type Output = Complex<usize>

The resulting type after applying the + operator.

fn add(self, other: Complex<usize>) -> Self::Output

Performs the + operation.

impl<'a, T: Clone + Num> Add<T> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the + operator.

fn add(self, other: T) -> Self::Output

Performs the + operation.

impl<T: Clone + Num> Add<T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the + operator.

fn add(self, other: T) -> Self::Output

Performs the + operation.

impl<T: Clone + Num> Add for Complex<T>

type Output = Complex<T>

The resulting type after applying the + operator.

fn add(self, other: Self) -> Self::Output

Performs the + operation.

impl<'a, T: Clone + NumAssign> AddAssign<&'a Complex<T>> for Complex<T>

fn add_assign(&mut self, other: &Self)

Performs the += operation.

impl<'a, T: Clone + NumAssign> AddAssign<&'a T> for Complex<T>

fn add_assign(&mut self, other: &T)

Performs the += operation.

impl<T: Clone + NumAssign> AddAssign<T> for Complex<T>

fn add_assign(&mut self, other: T)

Performs the += operation.

impl<T: Clone + NumAssign> AddAssign for Complex<T>

fn add_assign(&mut self, other: Self)

Performs the += operation.

impl<T, U> AsPrimitive<U> for Complex<T>

where T: AsPrimitive<U>, U: 'static + Copy,

fn as_(self) -> U

Convert a value to another, using the as operator.

impl<T> Binary for Complex<T>

where T: Binary + Num + PartialOrd + Clone,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T: Clone> Clone for Complex<T>

fn clone(&self) -> Complex<T>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<T: Debug> Debug for Complex<T>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T: Default> Default for Complex<T>

fn default() -> Complex<T>

Returns the “default value” for a type.

impl<T> Display for Complex<T>

where T: Display + Num + PartialOrd + Clone,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T, Re, Im> Distribution<Complex<T>> for ComplexDistribution<Re, Im>

where T: Num + Clone, Re: Distribution<T>, Im: Distribution<T>,

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Complex<T>

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T>

where R: Rng, Self: Sized,

Create an iterator that generates random values of T, using rng as the source of randomness.

fn map<F, S>(self, func: F) -> DistMap<Self, F, T, S>

where F: Fn(T) -> S, Self: Sized,

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F

impl<T> Distribution<Complex<T>> for Standard

where T: Num + Clone, Standard: Distribution<T>,

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Complex<T>

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T>

where R: Rng, Self: Sized,

Create an iterator that generates random values of T, using rng as the source of randomness.

fn map<F, S>(self, func: F) -> DistMap<Self, F, T, S>

where F: Fn(T) -> S, Self: Sized,

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F

impl<'a, 'b, T: Clone + Num> Div<&'b Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the / operator.

fn div(self, other: &Complex<T>) -> Self::Output

Performs the / operation.

impl<'a, T: Clone + Num> Div<&'a Complex<T>> for Complex<T>

type Output = Complex<T>

The resulting type after applying the / operator.

fn div(self, other: &Complex<T>) -> Self::Output

Performs the / operation.

impl<'a, 'b> Div<&'a Complex<f32>> for &'b f32

type Output = Complex<f32>

The resulting type after applying the / operator.

fn div(self, other: &Complex<f32>) -> Complex<f32>

Performs the / operation.

impl<'a> Div<&'a Complex<f32>> for f32

type Output = Complex<f32>

The resulting type after applying the / operator.

fn div(self, other: &Complex<f32>) -> Complex<f32>

Performs the / operation.

impl<'a, 'b> Div<&'a Complex<f64>> for &'b f64

type Output = Complex<f64>

The resulting type after applying the / operator.

fn div(self, other: &Complex<f64>) -> Complex<f64>

Performs the / operation.

impl<'a> Div<&'a Complex<f64>> for f64

type Output = Complex<f64>

The resulting type after applying the / operator.

fn div(self, other: &Complex<f64>) -> Complex<f64>

Performs the / operation.

impl<'a, 'b> Div<&'a Complex<i128>> for &'b i128

type Output = Complex<i128>

The resulting type after applying the / operator.

fn div(self, other: &Complex<i128>) -> Complex<i128>

Performs the / operation.

impl<'a> Div<&'a Complex<i128>> for i128

type Output = Complex<i128>

The resulting type after applying the / operator.

fn div(self, other: &Complex<i128>) -> Complex<i128>

Performs the / operation.

impl<'a, 'b> Div<&'a Complex<i16>> for &'b i16

type Output = Complex<i16>

The resulting type after applying the / operator.

fn div(self, other: &Complex<i16>) -> Complex<i16>

Performs the / operation.

impl<'a> Div<&'a Complex<i16>> for i16

type Output = Complex<i16>

The resulting type after applying the / operator.

fn div(self, other: &Complex<i16>) -> Complex<i16>

Performs the / operation.

impl<'a, 'b> Div<&'a Complex<i32>> for &'b i32

type Output = Complex<i32>

The resulting type after applying the / operator.

fn div(self, other: &Complex<i32>) -> Complex<i32>

Performs the / operation.

impl<'a> Div<&'a Complex<i32>> for i32

type Output = Complex<i32>

The resulting type after applying the / operator.

fn div(self, other: &Complex<i32>) -> Complex<i32>

Performs the / operation.

impl<'a, 'b> Div<&'a Complex<i64>> for &'b i64

type Output = Complex<i64>

The resulting type after applying the / operator.

fn div(self, other: &Complex<i64>) -> Complex<i64>

Performs the / operation.

impl<'a> Div<&'a Complex<i64>> for i64

type Output = Complex<i64>

The resulting type after applying the / operator.

fn div(self, other: &Complex<i64>) -> Complex<i64>

Performs the / operation.

impl<'a, 'b> Div<&'a Complex<i8>> for &'b i8

type Output = Complex<i8>

The resulting type after applying the / operator.

fn div(self, other: &Complex<i8>) -> Complex<i8>

Performs the / operation.

impl<'a> Div<&'a Complex<i8>> for i8

type Output = Complex<i8>

The resulting type after applying the / operator.

fn div(self, other: &Complex<i8>) -> Complex<i8>

Performs the / operation.

impl<'a, 'b> Div<&'a Complex<isize>> for &'b isize

type Output = Complex<isize>

The resulting type after applying the / operator.

fn div(self, other: &Complex<isize>) -> Complex<isize>

Performs the / operation.

impl<'a> Div<&'a Complex<isize>> for isize

type Output = Complex<isize>

The resulting type after applying the / operator.

fn div(self, other: &Complex<isize>) -> Complex<isize>

Performs the / operation.

impl<'a, 'b> Div<&'a Complex<u128>> for &'b u128

type Output = Complex<u128>

The resulting type after applying the / operator.

fn div(self, other: &Complex<u128>) -> Complex<u128>

Performs the / operation.

impl<'a> Div<&'a Complex<u128>> for u128

type Output = Complex<u128>

The resulting type after applying the / operator.

fn div(self, other: &Complex<u128>) -> Complex<u128>

Performs the / operation.

impl<'a, 'b> Div<&'a Complex<u16>> for &'b u16

type Output = Complex<u16>

The resulting type after applying the / operator.

fn div(self, other: &Complex<u16>) -> Complex<u16>

Performs the / operation.

impl<'a> Div<&'a Complex<u16>> for u16

type Output = Complex<u16>

The resulting type after applying the / operator.

fn div(self, other: &Complex<u16>) -> Complex<u16>

Performs the / operation.

impl<'a, 'b> Div<&'a Complex<u32>> for &'b u32

type Output = Complex<u32>

The resulting type after applying the / operator.

fn div(self, other: &Complex<u32>) -> Complex<u32>

Performs the / operation.

impl<'a> Div<&'a Complex<u32>> for u32

type Output = Complex<u32>

The resulting type after applying the / operator.

fn div(self, other: &Complex<u32>) -> Complex<u32>

Performs the / operation.

impl<'a, 'b> Div<&'a Complex<u64>> for &'b u64

type Output = Complex<u64>

The resulting type after applying the / operator.

fn div(self, other: &Complex<u64>) -> Complex<u64>

Performs the / operation.

impl<'a> Div<&'a Complex<u64>> for u64

type Output = Complex<u64>

The resulting type after applying the / operator.

fn div(self, other: &Complex<u64>) -> Complex<u64>

Performs the / operation.

impl<'a, 'b> Div<&'a Complex<u8>> for &'b u8

type Output = Complex<u8>

The resulting type after applying the / operator.

fn div(self, other: &Complex<u8>) -> Complex<u8>

Performs the / operation.

impl<'a> Div<&'a Complex<u8>> for u8

type Output = Complex<u8>

The resulting type after applying the / operator.

fn div(self, other: &Complex<u8>) -> Complex<u8>

Performs the / operation.

impl<'a, 'b> Div<&'a Complex<usize>> for &'b usize

type Output = Complex<usize>

The resulting type after applying the / operator.

fn div(self, other: &Complex<usize>) -> Complex<usize>

Performs the / operation.

impl<'a> Div<&'a Complex<usize>> for usize

type Output = Complex<usize>

The resulting type after applying the / operator.

fn div(self, other: &Complex<usize>) -> Complex<usize>

Performs the / operation.

impl<'a, 'b, T: Clone + Num> Div<&'a T> for &'b Complex<T>

type Output = Complex<T>

The resulting type after applying the / operator.

fn div(self, other: &T) -> Self::Output

Performs the / operation.

impl<'a, T: Clone + Num> Div<&'a T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the / operator.

fn div(self, other: &T) -> Self::Output

Performs the / operation.

impl<'a, T: Clone + Num> Div<Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the / operator.

fn div(self, other: Complex<T>) -> Self::Output

Performs the / operation.

impl<'a> Div<Complex<f32>> for &'a f32

type Output = Complex<f32>

The resulting type after applying the / operator.

fn div(self, other: Complex<f32>) -> Complex<f32>

Performs the / operation.

impl Div<Complex<f32>> for f32

type Output = Complex<f32>

The resulting type after applying the / operator.

fn div(self, other: Complex<f32>) -> Self::Output

Performs the / operation.

impl<'a> Div<Complex<f64>> for &'a f64

type Output = Complex<f64>

The resulting type after applying the / operator.

fn div(self, other: Complex<f64>) -> Complex<f64>

Performs the / operation.

impl Div<Complex<f64>> for f64

type Output = Complex<f64>

The resulting type after applying the / operator.

fn div(self, other: Complex<f64>) -> Self::Output

Performs the / operation.

impl<'a> Div<Complex<i128>> for &'a i128

type Output = Complex<i128>

The resulting type after applying the / operator.

fn div(self, other: Complex<i128>) -> Complex<i128>

Performs the / operation.

impl Div<Complex<i128>> for i128

type Output = Complex<i128>

The resulting type after applying the / operator.

fn div(self, other: Complex<i128>) -> Self::Output

Performs the / operation.

impl<'a> Div<Complex<i16>> for &'a i16

type Output = Complex<i16>

The resulting type after applying the / operator.

fn div(self, other: Complex<i16>) -> Complex<i16>

Performs the / operation.

impl Div<Complex<i16>> for i16

type Output = Complex<i16>

The resulting type after applying the / operator.

fn div(self, other: Complex<i16>) -> Self::Output

Performs the / operation.

impl<'a> Div<Complex<i32>> for &'a i32

type Output = Complex<i32>

The resulting type after applying the / operator.

fn div(self, other: Complex<i32>) -> Complex<i32>

Performs the / operation.

impl Div<Complex<i32>> for i32

type Output = Complex<i32>

The resulting type after applying the / operator.

fn div(self, other: Complex<i32>) -> Self::Output

Performs the / operation.

impl<'a> Div<Complex<i64>> for &'a i64

type Output = Complex<i64>

The resulting type after applying the / operator.

fn div(self, other: Complex<i64>) -> Complex<i64>

Performs the / operation.

impl Div<Complex<i64>> for i64

type Output = Complex<i64>

The resulting type after applying the / operator.

fn div(self, other: Complex<i64>) -> Self::Output

Performs the / operation.

impl<'a> Div<Complex<i8>> for &'a i8

type Output = Complex<i8>

The resulting type after applying the / operator.

fn div(self, other: Complex<i8>) -> Complex<i8>

Performs the / operation.

impl Div<Complex<i8>> for i8

type Output = Complex<i8>

The resulting type after applying the / operator.

fn div(self, other: Complex<i8>) -> Self::Output

Performs the / operation.

impl<'a> Div<Complex<isize>> for &'a isize

type Output = Complex<isize>

The resulting type after applying the / operator.

fn div(self, other: Complex<isize>) -> Complex<isize>

Performs the / operation.

impl Div<Complex<isize>> for isize

type Output = Complex<isize>

The resulting type after applying the / operator.

fn div(self, other: Complex<isize>) -> Self::Output

Performs the / operation.

impl<'a> Div<Complex<u128>> for &'a u128

type Output = Complex<u128>

The resulting type after applying the / operator.

fn div(self, other: Complex<u128>) -> Complex<u128>

Performs the / operation.

impl Div<Complex<u128>> for u128

type Output = Complex<u128>

The resulting type after applying the / operator.

fn div(self, other: Complex<u128>) -> Self::Output

Performs the / operation.

impl<'a> Div<Complex<u16>> for &'a u16

type Output = Complex<u16>

The resulting type after applying the / operator.

fn div(self, other: Complex<u16>) -> Complex<u16>

Performs the / operation.

impl Div<Complex<u16>> for u16

type Output = Complex<u16>

The resulting type after applying the / operator.

fn div(self, other: Complex<u16>) -> Self::Output

Performs the / operation.

impl<'a> Div<Complex<u32>> for &'a u32

type Output = Complex<u32>

The resulting type after applying the / operator.

fn div(self, other: Complex<u32>) -> Complex<u32>

Performs the / operation.

impl Div<Complex<u32>> for u32

type Output = Complex<u32>

The resulting type after applying the / operator.

fn div(self, other: Complex<u32>) -> Self::Output

Performs the / operation.

impl<'a> Div<Complex<u64>> for &'a u64

type Output = Complex<u64>

The resulting type after applying the / operator.

fn div(self, other: Complex<u64>) -> Complex<u64>

Performs the / operation.

impl Div<Complex<u64>> for u64

type Output = Complex<u64>

The resulting type after applying the / operator.

fn div(self, other: Complex<u64>) -> Self::Output

Performs the / operation.

impl<'a> Div<Complex<u8>> for &'a u8

type Output = Complex<u8>

The resulting type after applying the / operator.

fn div(self, other: Complex<u8>) -> Complex<u8>

Performs the / operation.

impl Div<Complex<u8>> for u8

type Output = Complex<u8>

The resulting type after applying the / operator.

fn div(self, other: Complex<u8>) -> Self::Output

Performs the / operation.

impl<'a> Div<Complex<usize>> for &'a usize

type Output = Complex<usize>

The resulting type after applying the / operator.

fn div(self, other: Complex<usize>) -> Complex<usize>

Performs the / operation.

impl Div<Complex<usize>> for usize

type Output = Complex<usize>

The resulting type after applying the / operator.

fn div(self, other: Complex<usize>) -> Self::Output

Performs the / operation.

impl<'a, T: Clone + Num> Div<T> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the / operator.

fn div(self, other: T) -> Self::Output

Performs the / operation.

impl<T: Clone + Num> Div<T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the / operator.

fn div(self, other: T) -> Self::Output

Performs the / operation.

impl<T: Clone + Num> Div for Complex<T>

type Output = Complex<T>

The resulting type after applying the / operator.

fn div(self, other: Self) -> Self::Output

Performs the / operation.

impl<'a, T: Clone + NumAssign> DivAssign<&'a Complex<T>> for Complex<T>

fn div_assign(&mut self, other: &Self)

Performs the /= operation.

impl<'a, T: Clone + NumAssign> DivAssign<&'a T> for Complex<T>

fn div_assign(&mut self, other: &T)

Performs the /= operation.

impl<T: Clone + NumAssign> DivAssign<T> for Complex<T>

fn div_assign(&mut self, other: T)

Performs the /= operation.

impl<T: Clone + NumAssign> DivAssign for Complex<T>

fn div_assign(&mut self, other: Self)

Performs the /= operation.

impl<'a, T: Clone + Num> From<&'a T> for Complex<T>

fn from(re: &T) -> Self

Converts to this type from the input type.

impl<T: Clone + Num> From<T> for Complex<T>

fn from(re: T) -> Self

Converts to this type from the input type.

impl<T: FromPrimitive + Num> FromPrimitive for Complex<T>

fn from_usize(n: usize) -> Option<Self>

Converts a usize to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_isize(n: isize) -> Option<Self>

Converts an isize to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u8(n: u8) -> Option<Self>

Converts an u8 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u16(n: u16) -> Option<Self>

Converts an u16 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u32(n: u32) -> Option<Self>

Converts an u32 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u64(n: u64) -> Option<Self>

Converts an u64 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i8(n: i8) -> Option<Self>

Converts an i8 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i16(n: i16) -> Option<Self>

Converts an i16 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i32(n: i32) -> Option<Self>

Converts an i32 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i64(n: i64) -> Option<Self>

Converts an i64 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u128(n: u128) -> Option<Self>

Converts an u128 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i128(n: i128) -> Option<Self>

Converts an i128 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_f32(n: f32) -> Option<Self>

Converts a f32 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_f64(n: f64) -> Option<Self>

Converts a f64 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

impl<T> FromStr for Complex<T>

where T: FromStr + Num + Clone,

fn from_str(s: &str) -> Result<Self, Self::Err>

Parses a +/- bi; ai +/- b; a; or bi where a and b are of type T

type Err = ParseComplexError<<T as FromStr>::Err>

The associated error which can be returned from parsing.

impl<T: Hash> Hash for Complex<T>

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl<'a, T: Clone + Num + Neg<Output = T>> Inv for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn inv(self) -> Self::Output

Returns the multiplicative inverse of self.

impl<T: Clone + Num + Neg<Output = T>> Inv for Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn inv(self) -> Self::Output

Returns the multiplicative inverse of self.

impl<T> LowerExp for Complex<T>

where T: LowerExp + Num + PartialOrd + Clone,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T> LowerHex for Complex<T>

where T: LowerHex + Num + PartialOrd + Clone,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<'a, 'b, T: Clone + Num> Mul<&'b Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<T>) -> Self::Output

Performs the * operation.

impl<'a, T: Clone + Num> Mul<&'a Complex<T>> for Complex<T>

type Output = Complex<T>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<T>) -> Self::Output

Performs the * operation.

impl<'a, 'b> Mul<&'a Complex<f32>> for &'b f32

type Output = Complex<f32>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<f32>) -> Complex<f32>

Performs the * operation.

impl<'a> Mul<&'a Complex<f32>> for f32

type Output = Complex<f32>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<f32>) -> Complex<f32>

Performs the * operation.

impl<'a, 'b> Mul<&'a Complex<f64>> for &'b f64

type Output = Complex<f64>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<f64>) -> Complex<f64>

Performs the * operation.

impl<'a> Mul<&'a Complex<f64>> for f64

type Output = Complex<f64>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<f64>) -> Complex<f64>

Performs the * operation.

impl<'a, 'b> Mul<&'a Complex<i128>> for &'b i128

type Output = Complex<i128>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<i128>) -> Complex<i128>

Performs the * operation.

impl<'a> Mul<&'a Complex<i128>> for i128

type Output = Complex<i128>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<i128>) -> Complex<i128>

Performs the * operation.

impl<'a, 'b> Mul<&'a Complex<i16>> for &'b i16

type Output = Complex<i16>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<i16>) -> Complex<i16>

Performs the * operation.

impl<'a> Mul<&'a Complex<i16>> for i16

type Output = Complex<i16>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<i16>) -> Complex<i16>

Performs the * operation.

impl<'a, 'b> Mul<&'a Complex<i32>> for &'b i32

type Output = Complex<i32>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<i32>) -> Complex<i32>

Performs the * operation.

impl<'a> Mul<&'a Complex<i32>> for i32

type Output = Complex<i32>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<i32>) -> Complex<i32>

Performs the * operation.

impl<'a, 'b> Mul<&'a Complex<i64>> for &'b i64

type Output = Complex<i64>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<i64>) -> Complex<i64>

Performs the * operation.

impl<'a> Mul<&'a Complex<i64>> for i64

type Output = Complex<i64>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<i64>) -> Complex<i64>

Performs the * operation.

impl<'a, 'b> Mul<&'a Complex<i8>> for &'b i8

type Output = Complex<i8>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<i8>) -> Complex<i8>

Performs the * operation.

impl<'a> Mul<&'a Complex<i8>> for i8

type Output = Complex<i8>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<i8>) -> Complex<i8>

Performs the * operation.

impl<'a, 'b> Mul<&'a Complex<isize>> for &'b isize

type Output = Complex<isize>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<isize>) -> Complex<isize>

Performs the * operation.

impl<'a> Mul<&'a Complex<isize>> for isize

type Output = Complex<isize>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<isize>) -> Complex<isize>

Performs the * operation.

impl<'a, 'b> Mul<&'a Complex<u128>> for &'b u128

type Output = Complex<u128>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<u128>) -> Complex<u128>

Performs the * operation.

impl<'a> Mul<&'a Complex<u128>> for u128

type Output = Complex<u128>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<u128>) -> Complex<u128>

Performs the * operation.

impl<'a, 'b> Mul<&'a Complex<u16>> for &'b u16

type Output = Complex<u16>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<u16>) -> Complex<u16>

Performs the * operation.

impl<'a> Mul<&'a Complex<u16>> for u16

type Output = Complex<u16>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<u16>) -> Complex<u16>

Performs the * operation.

impl<'a, 'b> Mul<&'a Complex<u32>> for &'b u32

type Output = Complex<u32>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<u32>) -> Complex<u32>

Performs the * operation.

impl<'a> Mul<&'a Complex<u32>> for u32

type Output = Complex<u32>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<u32>) -> Complex<u32>

Performs the * operation.

impl<'a, 'b> Mul<&'a Complex<u64>> for &'b u64

type Output = Complex<u64>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<u64>) -> Complex<u64>

Performs the * operation.

impl<'a> Mul<&'a Complex<u64>> for u64

type Output = Complex<u64>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<u64>) -> Complex<u64>

Performs the * operation.

impl<'a, 'b> Mul<&'a Complex<u8>> for &'b u8

type Output = Complex<u8>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<u8>) -> Complex<u8>

Performs the * operation.

impl<'a> Mul<&'a Complex<u8>> for u8

type Output = Complex<u8>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<u8>) -> Complex<u8>

Performs the * operation.

impl<'a, 'b> Mul<&'a Complex<usize>> for &'b usize

type Output = Complex<usize>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<usize>) -> Complex<usize>

Performs the * operation.

impl<'a> Mul<&'a Complex<usize>> for usize

type Output = Complex<usize>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<usize>) -> Complex<usize>

Performs the * operation.

impl<'a, 'b, T: Clone + Num> Mul<&'a T> for &'b Complex<T>

type Output = Complex<T>

The resulting type after applying the * operator.

fn mul(self, other: &T) -> Self::Output

Performs the * operation.

impl<'a, T: Clone + Num> Mul<&'a T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the * operator.

fn mul(self, other: &T) -> Self::Output

Performs the * operation.

impl<'a, T: Clone + Num> Mul<Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the * operator.

fn mul(self, other: Complex<T>) -> Self::Output

Performs the * operation.

impl<'a> Mul<Complex<f32>> for &'a f32

type Output = Complex<f32>

The resulting type after applying the * operator.

fn mul(self, other: Complex<f32>) -> Complex<f32>

Performs the * operation.

impl Mul<Complex<f32>> for f32

type Output = Complex<f32>

The resulting type after applying the * operator.

fn mul(self, other: Complex<f32>) -> Self::Output

Performs the * operation.

impl<'a> Mul<Complex<f64>> for &'a f64

type Output = Complex<f64>

The resulting type after applying the * operator.

fn mul(self, other: Complex<f64>) -> Complex<f64>

Performs the * operation.

impl Mul<Complex<f64>> for f64

type Output = Complex<f64>

The resulting type after applying the * operator.

fn mul(self, other: Complex<f64>) -> Self::Output

Performs the * operation.

impl<'a> Mul<Complex<i128>> for &'a i128

type Output = Complex<i128>

The resulting type after applying the * operator.

fn mul(self, other: Complex<i128>) -> Complex<i128>

Performs the * operation.

impl Mul<Complex<i128>> for i128

type Output = Complex<i128>

The resulting type after applying the * operator.

fn mul(self, other: Complex<i128>) -> Self::Output

Performs the * operation.

impl<'a> Mul<Complex<i16>> for &'a i16

type Output = Complex<i16>

The resulting type after applying the * operator.

fn mul(self, other: Complex<i16>) -> Complex<i16>

Performs the * operation.

impl Mul<Complex<i16>> for i16

type Output = Complex<i16>

The resulting type after applying the * operator.

fn mul(self, other: Complex<i16>) -> Self::Output

Performs the * operation.

impl<'a> Mul<Complex<i32>> for &'a i32

type Output = Complex<i32>

The resulting type after applying the * operator.

fn mul(self, other: Complex<i32>) -> Complex<i32>

Performs the * operation.

impl Mul<Complex<i32>> for i32

type Output = Complex<i32>

The resulting type after applying the * operator.

fn mul(self, other: Complex<i32>) -> Self::Output

Performs the * operation.

impl<'a> Mul<Complex<i64>> for &'a i64

type Output = Complex<i64>

The resulting type after applying the * operator.

fn mul(self, other: Complex<i64>) -> Complex<i64>

Performs the * operation.

impl Mul<Complex<i64>> for i64

type Output = Complex<i64>

The resulting type after applying the * operator.

fn mul(self, other: Complex<i64>) -> Self::Output

Performs the * operation.

impl<'a> Mul<Complex<i8>> for &'a i8

type Output = Complex<i8>

The resulting type after applying the * operator.

fn mul(self, other: Complex<i8>) -> Complex<i8>

Performs the * operation.

impl Mul<Complex<i8>> for i8

type Output = Complex<i8>

The resulting type after applying the * operator.

fn mul(self, other: Complex<i8>) -> Self::Output

Performs the * operation.

impl<'a> Mul<Complex<isize>> for &'a isize

type Output = Complex<isize>

The resulting type after applying the * operator.

fn mul(self, other: Complex<isize>) -> Complex<isize>

Performs the * operation.

impl Mul<Complex<isize>> for isize

type Output = Complex<isize>

The resulting type after applying the * operator.

fn mul(self, other: Complex<isize>) -> Self::Output

Performs the * operation.

impl<'a> Mul<Complex<u128>> for &'a u128

type Output = Complex<u128>

The resulting type after applying the * operator.

fn mul(self, other: Complex<u128>) -> Complex<u128>

Performs the * operation.

impl Mul<Complex<u128>> for u128

type Output = Complex<u128>

The resulting type after applying the * operator.

fn mul(self, other: Complex<u128>) -> Self::Output

Performs the * operation.

impl<'a> Mul<Complex<u16>> for &'a u16

type Output = Complex<u16>

The resulting type after applying the * operator.

fn mul(self, other: Complex<u16>) -> Complex<u16>

Performs the * operation.

impl Mul<Complex<u16>> for u16

type Output = Complex<u16>

The resulting type after applying the * operator.

fn mul(self, other: Complex<u16>) -> Self::Output

Performs the * operation.

impl<'a> Mul<Complex<u32>> for &'a u32

type Output = Complex<u32>

The resulting type after applying the * operator.

fn mul(self, other: Complex<u32>) -> Complex<u32>

Performs the * operation.

impl Mul<Complex<u32>> for u32

type Output = Complex<u32>

The resulting type after applying the * operator.

fn mul(self, other: Complex<u32>) -> Self::Output

Performs the * operation.

impl<'a> Mul<Complex<u64>> for &'a u64

type Output = Complex<u64>

The resulting type after applying the * operator.

fn mul(self, other: Complex<u64>) -> Complex<u64>

Performs the * operation.

impl Mul<Complex<u64>> for u64

type Output = Complex<u64>

The resulting type after applying the * operator.

fn mul(self, other: Complex<u64>) -> Self::Output

Performs the * operation.

impl<'a> Mul<Complex<u8>> for &'a u8

type Output = Complex<u8>

The resulting type after applying the * operator.

fn mul(self, other: Complex<u8>) -> Complex<u8>

Performs the * operation.

impl Mul<Complex<u8>> for u8

type Output = Complex<u8>

The resulting type after applying the * operator.

fn mul(self, other: Complex<u8>) -> Self::Output

Performs the * operation.

impl<'a> Mul<Complex<usize>> for &'a usize

type Output = Complex<usize>

The resulting type after applying the * operator.

fn mul(self, other: Complex<usize>) -> Complex<usize>

Performs the * operation.

impl Mul<Complex<usize>> for usize

type Output = Complex<usize>

The resulting type after applying the * operator.

fn mul(self, other: Complex<usize>) -> Self::Output

Performs the * operation.

impl<'a, T: Clone + Num> Mul<T> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the * operator.

fn mul(self, other: T) -> Self::Output

Performs the * operation.

impl<T: Clone + Num> Mul<T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the * operator.

fn mul(self, other: T) -> Self::Output

Performs the * operation.

impl<T: Clone + Num> Mul for Complex<T>

type Output = Complex<T>

The resulting type after applying the * operator.

fn mul(self, other: Self) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: Clone + Num + MulAdd<Output = T>> MulAdd<&'b Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the fused multiply-add.

fn mul_add(self, other: &Complex<T>, add: &Complex<T>) -> Complex<T>

Performs the fused multiply-add operation (self * a) + b

impl<T: Clone + Num + MulAdd<Output = T>> MulAdd for Complex<T>

type Output = Complex<T>

The resulting type after applying the fused multiply-add.

fn mul_add(self, other: Complex<T>, add: Complex<T>) -> Complex<T>

Performs the fused multiply-add operation (self * a) + b

impl<'a, 'b, T: Clone + NumAssign + MulAddAssign> MulAddAssign<&'a Complex<T>, &'b Complex<T>> for Complex<T>

fn mul_add_assign(&mut self, other: &Complex<T>, add: &Complex<T>)

Performs the fused multiply-add assignment operation *self = (*self * a) + b

impl<T: Clone + NumAssign + MulAddAssign> MulAddAssign for Complex<T>

fn mul_add_assign(&mut self, other: Complex<T>, add: Complex<T>)

Performs the fused multiply-add assignment operation *self = (*self * a) + b

impl<'a, T: Clone + NumAssign> MulAssign<&'a Complex<T>> for Complex<T>

fn mul_assign(&mut self, other: &Self)

Performs the *= operation.

impl<'a, T: Clone + NumAssign> MulAssign<&'a T> for Complex<T>

fn mul_assign(&mut self, other: &T)

Performs the *= operation.

impl<T: Clone + NumAssign> MulAssign<T> for Complex<T>

fn mul_assign(&mut self, other: T)

Performs the *= operation.

impl<T: Clone + NumAssign> MulAssign for Complex<T>

fn mul_assign(&mut self, other: Self)

Performs the *= operation.

impl<'a, T: Clone + Num + Neg<Output = T>> Neg for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<T: Clone + Num + Neg<Output = T>> Neg for Complex<T>

type Output = Complex<T>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<T: Num + Clone> Num for Complex<T>

fn from_str_radix(s: &str, radix: u32) -> Result<Self, Self::FromStrRadixErr>

Parses a +/- bi; ai +/- b; a; or bi where a and b are of type T

type FromStrRadixErr = ParseComplexError<<T as Num>::FromStrRadixErr>

impl<T: NumCast + Num> NumCast for Complex<T>

fn from<U: ToPrimitive>(n: U) -> Option<Self>

Creates a number from another value that can be converted into a primitive via the ToPrimitive trait. If the source value cannot be represented by the target type, then None is returned.

impl<T> Octal for Complex<T>

where T: Octal + Num + PartialOrd + Clone,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T: Clone + Num> One for Complex<T>

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

Returns true if self is equal to the multiplicative identity.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

impl<T: PartialEq> PartialEq for Complex<T>

fn eq(&self, other: &Complex<T>) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<'a, 'b, T: Float> Pow<&'b Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &'b Complex<T>) -> Self::Output

Returns self to the power rhs.

impl<'b, T: Float> Pow<&'b Complex<T>> for Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &'b Complex<T>) -> Self::Output

Returns self to the power rhs.

impl<'a, 'b, T: Float> Pow<&'b f32> for &'a Complex<T>

where f32: Into<T>,

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &f32) -> Self::Output

Returns self to the power rhs.

impl<'b, T: Float> Pow<&'b f32> for Complex<T>

where f32: Into<T>,

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &f32) -> Self::Output

Returns self to the power rhs.

impl<'a, 'b, T: Float> Pow<&'b f64> for &'a Complex<T>

where f64: Into<T>,

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &f64) -> Self::Output

Returns self to the power rhs.

impl<'b, T: Float> Pow<&'b f64> for Complex<T>

where f64: Into<T>,

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &f64) -> Self::Output

Returns self to the power rhs.

impl<'a, 'b, T: Clone + Num + Neg<Output = T>> Pow<&'b i128> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &i128) -> Self::Output

Returns self to the power rhs.

impl<'a, 'b, T: Clone + Num + Neg<Output = T>> Pow<&'b i16> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &i16) -> Self::Output

Returns self to the power rhs.

impl<'a, 'b, T: Clone + Num + Neg<Output = T>> Pow<&'b i32> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &i32) -> Self::Output

Returns self to the power rhs.

impl<'a, 'b, T: Clone + Num + Neg<Output = T>> Pow<&'b i64> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &i64) -> Self::Output

Returns self to the power rhs.

impl<'a, 'b, T: Clone + Num + Neg<Output = T>> Pow<&'b i8> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &i8) -> Self::Output

Returns self to the power rhs.

impl<'a, 'b, T: Clone + Num + Neg<Output = T>> Pow<&'b isize> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &isize) -> Self::Output

Returns self to the power rhs.

impl<'a, 'b, T: Clone + Num> Pow<&'b u128> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &u128) -> Self::Output

Returns self to the power rhs.

impl<'a, 'b, T: Clone + Num> Pow<&'b u16> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &u16) -> Self::Output

Returns self to the power rhs.

impl<'a, 'b, T: Clone + Num> Pow<&'b u32> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &u32) -> Self::Output

Returns self to the power rhs.

impl<'a, 'b, T: Clone + Num> Pow<&'b u64> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &u64) -> Self::Output

Returns self to the power rhs.

impl<'a, 'b, T: Clone + Num> Pow<&'b u8> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &u8) -> Self::Output

Returns self to the power rhs.

impl<'a, 'b, T: Clone + Num> Pow<&'b usize> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: &usize) -> Self::Output

Returns self to the power rhs.

impl<'a, T: Float> Pow<Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: Complex<T>) -> Self::Output

Returns self to the power rhs.

impl<T: Float> Pow<Complex<T>> for Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: Complex<T>) -> Self::Output

Returns self to the power rhs.

impl<'a, T: Float> Pow<f32> for &'a Complex<T>

where f32: Into<T>,

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: f32) -> Self::Output

Returns self to the power rhs.

impl<T: Float> Pow<f32> for Complex<T>

where f32: Into<T>,

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: f32) -> Self::Output

Returns self to the power rhs.

impl<'a, T: Float> Pow<f64> for &'a Complex<T>

where f64: Into<T>,

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: f64) -> Self::Output

Returns self to the power rhs.

impl<T: Float> Pow<f64> for Complex<T>

where f64: Into<T>,

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: f64) -> Self::Output

Returns self to the power rhs.

impl<'a, T: Clone + Num + Neg<Output = T>> Pow<i128> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: i128) -> Self::Output

Returns self to the power rhs.

impl<'a, T: Clone + Num + Neg<Output = T>> Pow<i16> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: i16) -> Self::Output

Returns self to the power rhs.

impl<'a, T: Clone + Num + Neg<Output = T>> Pow<i32> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: i32) -> Self::Output

Returns self to the power rhs.

impl<'a, T: Clone + Num + Neg<Output = T>> Pow<i64> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: i64) -> Self::Output

Returns self to the power rhs.

impl<'a, T: Clone + Num + Neg<Output = T>> Pow<i8> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: i8) -> Self::Output

Returns self to the power rhs.

impl<'a, T: Clone + Num + Neg<Output = T>> Pow<isize> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: isize) -> Self::Output

Returns self to the power rhs.

impl<'a, T: Clone + Num> Pow<u128> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: u128) -> Self::Output

Returns self to the power rhs.

impl<'a, T: Clone + Num> Pow<u16> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: u16) -> Self::Output

Returns self to the power rhs.

impl<'a, T: Clone + Num> Pow<u32> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: u32) -> Self::Output

Returns self to the power rhs.

impl<'a, T: Clone + Num> Pow<u64> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: u64) -> Self::Output

Returns self to the power rhs.

impl<'a, T: Clone + Num> Pow<u8> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: u8) -> Self::Output

Returns self to the power rhs.

impl<'a, T: Clone + Num> Pow<usize> for &'a Complex<T>

type Output = Complex<T>

The result after applying the operator.

fn pow(self, exp: usize) -> Self::Output

Returns self to the power rhs.

impl<'a, T: 'a + Num + Clone> Product<&'a Complex<T>> for Complex<T>

fn product<I>(iter: I) -> Self

where I: Iterator<Item = &'a Complex<T>>,

Takes an iterator and generates Self from the elements by multiplying the items.

impl<T: Num + Clone> Product for Complex<T>

fn product<I>(iter: I) -> Self

where I: Iterator<Item = Self>,

Takes an iterator and generates Self from the elements by multiplying the items.

impl<'a, 'b, T: Clone + Num> Rem<&'b Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<T>) -> Self::Output

Performs the % operation.

impl<'a, T: Clone + Num> Rem<&'a Complex<T>> for Complex<T>

type Output = Complex<T>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<T>) -> Self::Output

Performs the % operation.

impl<'a, 'b> Rem<&'a Complex<f32>> for &'b f32

type Output = Complex<f32>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<f32>) -> Complex<f32>

Performs the % operation.

impl<'a> Rem<&'a Complex<f32>> for f32

type Output = Complex<f32>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<f32>) -> Complex<f32>

Performs the % operation.

impl<'a, 'b> Rem<&'a Complex<f64>> for &'b f64

type Output = Complex<f64>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<f64>) -> Complex<f64>

Performs the % operation.

impl<'a> Rem<&'a Complex<f64>> for f64

type Output = Complex<f64>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<f64>) -> Complex<f64>

Performs the % operation.

impl<'a, 'b> Rem<&'a Complex<i128>> for &'b i128

type Output = Complex<i128>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<i128>) -> Complex<i128>

Performs the % operation.

impl<'a> Rem<&'a Complex<i128>> for i128

type Output = Complex<i128>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<i128>) -> Complex<i128>

Performs the % operation.

impl<'a, 'b> Rem<&'a Complex<i16>> for &'b i16

type Output = Complex<i16>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<i16>) -> Complex<i16>

Performs the % operation.

impl<'a> Rem<&'a Complex<i16>> for i16

type Output = Complex<i16>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<i16>) -> Complex<i16>

Performs the % operation.

impl<'a, 'b> Rem<&'a Complex<i32>> for &'b i32

type Output = Complex<i32>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<i32>) -> Complex<i32>

Performs the % operation.

impl<'a> Rem<&'a Complex<i32>> for i32

type Output = Complex<i32>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<i32>) -> Complex<i32>

Performs the % operation.

impl<'a, 'b> Rem<&'a Complex<i64>> for &'b i64

type Output = Complex<i64>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<i64>) -> Complex<i64>

Performs the % operation.

impl<'a> Rem<&'a Complex<i64>> for i64

type Output = Complex<i64>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<i64>) -> Complex<i64>

Performs the % operation.

impl<'a, 'b> Rem<&'a Complex<i8>> for &'b i8

type Output = Complex<i8>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<i8>) -> Complex<i8>

Performs the % operation.

impl<'a> Rem<&'a Complex<i8>> for i8

type Output = Complex<i8>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<i8>) -> Complex<i8>

Performs the % operation.

impl<'a, 'b> Rem<&'a Complex<isize>> for &'b isize

type Output = Complex<isize>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<isize>) -> Complex<isize>

Performs the % operation.

impl<'a> Rem<&'a Complex<isize>> for isize

type Output = Complex<isize>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<isize>) -> Complex<isize>

Performs the % operation.

impl<'a, 'b> Rem<&'a Complex<u128>> for &'b u128

type Output = Complex<u128>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<u128>) -> Complex<u128>

Performs the % operation.

impl<'a> Rem<&'a Complex<u128>> for u128

type Output = Complex<u128>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<u128>) -> Complex<u128>

Performs the % operation.

impl<'a, 'b> Rem<&'a Complex<u16>> for &'b u16

type Output = Complex<u16>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<u16>) -> Complex<u16>

Performs the % operation.

impl<'a> Rem<&'a Complex<u16>> for u16

type Output = Complex<u16>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<u16>) -> Complex<u16>

Performs the % operation.

impl<'a, 'b> Rem<&'a Complex<u32>> for &'b u32

type Output = Complex<u32>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<u32>) -> Complex<u32>

Performs the % operation.

impl<'a> Rem<&'a Complex<u32>> for u32

type Output = Complex<u32>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<u32>) -> Complex<u32>

Performs the % operation.

impl<'a, 'b> Rem<&'a Complex<u64>> for &'b u64

type Output = Complex<u64>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<u64>) -> Complex<u64>

Performs the % operation.

impl<'a> Rem<&'a Complex<u64>> for u64

type Output = Complex<u64>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<u64>) -> Complex<u64>

Performs the % operation.

impl<'a, 'b> Rem<&'a Complex<u8>> for &'b u8

type Output = Complex<u8>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<u8>) -> Complex<u8>

Performs the % operation.

impl<'a> Rem<&'a Complex<u8>> for u8

type Output = Complex<u8>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<u8>) -> Complex<u8>

Performs the % operation.

impl<'a, 'b> Rem<&'a Complex<usize>> for &'b usize

type Output = Complex<usize>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<usize>) -> Complex<usize>

Performs the % operation.

impl<'a> Rem<&'a Complex<usize>> for usize

type Output = Complex<usize>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<usize>) -> Complex<usize>

Performs the % operation.

impl<'a, 'b, T: Clone + Num> Rem<&'a T> for &'b Complex<T>

type Output = Complex<T>

The resulting type after applying the % operator.

fn rem(self, other: &T) -> Self::Output

Performs the % operation.

impl<'a, T: Clone + Num> Rem<&'a T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the % operator.

fn rem(self, other: &T) -> Self::Output

Performs the % operation.

impl<'a, T: Clone + Num> Rem<Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the % operator.

fn rem(self, other: Complex<T>) -> Self::Output

Performs the % operation.

impl<'a> Rem<Complex<f32>> for &'a f32

type Output = Complex<f32>

The resulting type after applying the % operator.

fn rem(self, other: Complex<f32>) -> Complex<f32>

Performs the % operation.

impl Rem<Complex<f32>> for f32

type Output = Complex<f32>

The resulting type after applying the % operator.

fn rem(self, other: Complex<f32>) -> Self::Output

Performs the % operation.

impl<'a> Rem<Complex<f64>> for &'a f64

type Output = Complex<f64>

The resulting type after applying the % operator.

fn rem(self, other: Complex<f64>) -> Complex<f64>

Performs the % operation.

impl Rem<Complex<f64>> for f64

type Output = Complex<f64>

The resulting type after applying the % operator.

fn rem(self, other: Complex<f64>) -> Self::Output

Performs the % operation.

impl<'a> Rem<Complex<i128>> for &'a i128

type Output = Complex<i128>

The resulting type after applying the % operator.

fn rem(self, other: Complex<i128>) -> Complex<i128>

Performs the % operation.

impl Rem<Complex<i128>> for i128

type Output = Complex<i128>

The resulting type after applying the % operator.

fn rem(self, other: Complex<i128>) -> Self::Output

Performs the % operation.

impl<'a> Rem<Complex<i16>> for &'a i16

type Output = Complex<i16>

The resulting type after applying the % operator.

fn rem(self, other: Complex<i16>) -> Complex<i16>

Performs the % operation.

impl Rem<Complex<i16>> for i16

type Output = Complex<i16>

The resulting type after applying the % operator.

fn rem(self, other: Complex<i16>) -> Self::Output

Performs the % operation.

impl<'a> Rem<Complex<i32>> for &'a i32

type Output = Complex<i32>

The resulting type after applying the % operator.

fn rem(self, other: Complex<i32>) -> Complex<i32>

Performs the % operation.

impl Rem<Complex<i32>> for i32

type Output = Complex<i32>

The resulting type after applying the % operator.

fn rem(self, other: Complex<i32>) -> Self::Output

Performs the % operation.

impl<'a> Rem<Complex<i64>> for &'a i64

type Output = Complex<i64>

The resulting type after applying the % operator.

fn rem(self, other: Complex<i64>) -> Complex<i64>

Performs the % operation.

impl Rem<Complex<i64>> for i64

type Output = Complex<i64>

The resulting type after applying the % operator.

fn rem(self, other: Complex<i64>) -> Self::Output

Performs the % operation.

impl<'a> Rem<Complex<i8>> for &'a i8

type Output = Complex<i8>

The resulting type after applying the % operator.

fn rem(self, other: Complex<i8>) -> Complex<i8>

Performs the % operation.

impl Rem<Complex<i8>> for i8

type Output = Complex<i8>

The resulting type after applying the % operator.

fn rem(self, other: Complex<i8>) -> Self::Output

Performs the % operation.

impl<'a> Rem<Complex<isize>> for &'a isize

type Output = Complex<isize>

The resulting type after applying the % operator.

fn rem(self, other: Complex<isize>) -> Complex<isize>

Performs the % operation.

impl Rem<Complex<isize>> for isize

type Output = Complex<isize>

The resulting type after applying the % operator.

fn rem(self, other: Complex<isize>) -> Self::Output

Performs the % operation.

impl<'a> Rem<Complex<u128>> for &'a u128

type Output = Complex<u128>

The resulting type after applying the % operator.

fn rem(self, other: Complex<u128>) -> Complex<u128>

Performs the % operation.

impl Rem<Complex<u128>> for u128

type Output = Complex<u128>

The resulting type after applying the % operator.

fn rem(self, other: Complex<u128>) -> Self::Output

Performs the % operation.

impl<'a> Rem<Complex<u16>> for &'a u16

type Output = Complex<u16>

The resulting type after applying the % operator.

fn rem(self, other: Complex<u16>) -> Complex<u16>

Performs the % operation.

impl Rem<Complex<u16>> for u16

type Output = Complex<u16>

The resulting type after applying the % operator.

fn rem(self, other: Complex<u16>) -> Self::Output

Performs the % operation.

impl<'a> Rem<Complex<u32>> for &'a u32

type Output = Complex<u32>

The resulting type after applying the % operator.

fn rem(self, other: Complex<u32>) -> Complex<u32>

Performs the % operation.

impl Rem<Complex<u32>> for u32

type Output = Complex<u32>

The resulting type after applying the % operator.

fn rem(self, other: Complex<u32>) -> Self::Output

Performs the % operation.

impl<'a> Rem<Complex<u64>> for &'a u64

type Output = Complex<u64>

The resulting type after applying the % operator.

fn rem(self, other: Complex<u64>) -> Complex<u64>

Performs the % operation.

impl Rem<Complex<u64>> for u64

type Output = Complex<u64>

The resulting type after applying the % operator.

fn rem(self, other: Complex<u64>) -> Self::Output

Performs the % operation.

impl<'a> Rem<Complex<u8>> for &'a u8

type Output = Complex<u8>

The resulting type after applying the % operator.

fn rem(self, other: Complex<u8>) -> Complex<u8>

Performs the % operation.

impl Rem<Complex<u8>> for u8

type Output = Complex<u8>

The resulting type after applying the % operator.

fn rem(self, other: Complex<u8>) -> Self::Output

Performs the % operation.

impl<'a> Rem<Complex<usize>> for &'a usize

type Output = Complex<usize>

The resulting type after applying the % operator.

fn rem(self, other: Complex<usize>) -> Complex<usize>

Performs the % operation.

impl Rem<Complex<usize>> for usize

type Output = Complex<usize>

The resulting type after applying the % operator.

fn rem(self, other: Complex<usize>) -> Self::Output

Performs the % operation.

impl<'a, T: Clone + Num> Rem<T> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the % operator.

fn rem(self, other: T) -> Self::Output

Performs the % operation.

impl<T: Clone + Num> Rem<T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the % operator.

fn rem(self, other: T) -> Self::Output

Performs the % operation.

impl<T: Clone + Num> Rem for Complex<T>

type Output = Complex<T>

The resulting type after applying the % operator.

fn rem(self, modulus: Self) -> Self::Output

Performs the % operation.

impl<'a, T: Clone + NumAssign> RemAssign<&'a Complex<T>> for Complex<T>

fn rem_assign(&mut self, other: &Self)

Performs the %= operation.

impl<'a, T: Clone + NumAssign> RemAssign<&'a T> for Complex<T>

fn rem_assign(&mut self, other: &T)

Performs the %= operation.

impl<T: Clone + NumAssign> RemAssign<T> for Complex<T>

fn rem_assign(&mut self, other: T)

Performs the %= operation.

impl<T: Clone + NumAssign> RemAssign for Complex<T>

fn rem_assign(&mut self, modulus: Self)

Performs the %= operation.

impl<'a, 'b, T: Clone + Num> Sub<&'b Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<T>) -> Self::Output

Performs the - operation.

impl<'a, T: Clone + Num> Sub<&'a Complex<T>> for Complex<T>

type Output = Complex<T>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<T>) -> Self::Output

Performs the - operation.

impl<'a, 'b> Sub<&'a Complex<f32>> for &'b f32

type Output = Complex<f32>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<f32>) -> Complex<f32>

Performs the - operation.

impl<'a> Sub<&'a Complex<f32>> for f32

type Output = Complex<f32>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<f32>) -> Complex<f32>

Performs the - operation.

impl<'a, 'b> Sub<&'a Complex<f64>> for &'b f64

type Output = Complex<f64>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<f64>) -> Complex<f64>

Performs the - operation.

impl<'a> Sub<&'a Complex<f64>> for f64

type Output = Complex<f64>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<f64>) -> Complex<f64>

Performs the - operation.

impl<'a, 'b> Sub<&'a Complex<i128>> for &'b i128

type Output = Complex<i128>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<i128>) -> Complex<i128>

Performs the - operation.

impl<'a> Sub<&'a Complex<i128>> for i128

type Output = Complex<i128>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<i128>) -> Complex<i128>

Performs the - operation.

impl<'a, 'b> Sub<&'a Complex<i16>> for &'b i16

type Output = Complex<i16>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<i16>) -> Complex<i16>

Performs the - operation.

impl<'a> Sub<&'a Complex<i16>> for i16

type Output = Complex<i16>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<i16>) -> Complex<i16>

Performs the - operation.

impl<'a, 'b> Sub<&'a Complex<i32>> for &'b i32

type Output = Complex<i32>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<i32>) -> Complex<i32>

Performs the - operation.

impl<'a> Sub<&'a Complex<i32>> for i32

type Output = Complex<i32>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<i32>) -> Complex<i32>

Performs the - operation.

impl<'a, 'b> Sub<&'a Complex<i64>> for &'b i64

type Output = Complex<i64>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<i64>) -> Complex<i64>

Performs the - operation.

impl<'a> Sub<&'a Complex<i64>> for i64

type Output = Complex<i64>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<i64>) -> Complex<i64>

Performs the - operation.

impl<'a, 'b> Sub<&'a Complex<i8>> for &'b i8

type Output = Complex<i8>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<i8>) -> Complex<i8>

Performs the - operation.

impl<'a> Sub<&'a Complex<i8>> for i8

type Output = Complex<i8>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<i8>) -> Complex<i8>

Performs the - operation.

impl<'a, 'b> Sub<&'a Complex<isize>> for &'b isize

type Output = Complex<isize>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<isize>) -> Complex<isize>

Performs the - operation.

impl<'a> Sub<&'a Complex<isize>> for isize

type Output = Complex<isize>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<isize>) -> Complex<isize>

Performs the - operation.

impl<'a, 'b> Sub<&'a Complex<u128>> for &'b u128

type Output = Complex<u128>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<u128>) -> Complex<u128>

Performs the - operation.

impl<'a> Sub<&'a Complex<u128>> for u128

type Output = Complex<u128>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<u128>) -> Complex<u128>

Performs the - operation.

impl<'a, 'b> Sub<&'a Complex<u16>> for &'b u16

type Output = Complex<u16>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<u16>) -> Complex<u16>

Performs the - operation.

impl<'a> Sub<&'a Complex<u16>> for u16

type Output = Complex<u16>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<u16>) -> Complex<u16>

Performs the - operation.

impl<'a, 'b> Sub<&'a Complex<u32>> for &'b u32

type Output = Complex<u32>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<u32>) -> Complex<u32>

Performs the - operation.

impl<'a> Sub<&'a Complex<u32>> for u32

type Output = Complex<u32>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<u32>) -> Complex<u32>

Performs the - operation.

impl<'a, 'b> Sub<&'a Complex<u64>> for &'b u64

type Output = Complex<u64>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<u64>) -> Complex<u64>

Performs the - operation.

impl<'a> Sub<&'a Complex<u64>> for u64

type Output = Complex<u64>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<u64>) -> Complex<u64>

Performs the - operation.

impl<'a, 'b> Sub<&'a Complex<u8>> for &'b u8

type Output = Complex<u8>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<u8>) -> Complex<u8>

Performs the - operation.

impl<'a> Sub<&'a Complex<u8>> for u8

type Output = Complex<u8>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<u8>) -> Complex<u8>

Performs the - operation.

impl<'a, 'b> Sub<&'a Complex<usize>> for &'b usize

type Output = Complex<usize>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<usize>) -> Complex<usize>

Performs the - operation.

impl<'a> Sub<&'a Complex<usize>> for usize

type Output = Complex<usize>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<usize>) -> Complex<usize>

Performs the - operation.

impl<'a, 'b, T: Clone + Num> Sub<&'a T> for &'b Complex<T>

type Output = Complex<T>

The resulting type after applying the - operator.

fn sub(self, other: &T) -> Self::Output

Performs the - operation.

impl<'a, T: Clone + Num> Sub<&'a T> for Complex<T>

type Output = Complex<T>

The resulting type after applying the - operator.

fn sub(self, other: &T) -> Self::Output

Performs the - operation.

impl<'a, T: Clone + Num> Sub<Complex<T>> for &'a Complex<T>

type Output = Complex<T>

The resulting type after applying the - operator.

fn sub(self, other: Complex<T>) -> Self::Output

Performs the - operation.

impl<'a> Sub<Complex<f32>> for &'a f32

type Output = Complex<f32>

The resulting type after applying the - operator.

fn sub(self, other: Complex<f32>) -> Complex<f32>

Performs the - operation.

impl Sub<Complex<f32>> for f32

type Output = Complex<f32>

The resulting type after applying the - operator.

fn sub(self, other: Complex<f32>) -> Self::Output

Performs the - operation.

impl<'a> Sub<Complex<f64>> for &'a f64

type Output = Complex<f64>

The resulting type after applying the - operator.

fn sub(self, other: Complex<f64>) -> Complex<f64>

Performs the - operation.

impl Sub<Complex<f64>> for f64

type Output = Complex<f64>

The resulting type after applying the - operator.

fn sub(self, other: Complex<f64>) -> Self::Output

Performs the - operation.

impl<'a> Sub<Complex<i128>> for &'a i128

type Output = Complex<i128>

The resulting type after applying the - operator.

fn sub(self, other: Complex<i128>) -> Complex<i128>

Performs the - operation.

impl Sub<Complex<i128>> for i128

type Output = Complex<i128>

The resulting type after applying the - operator.

fn sub(self, other: Complex<i128>) -> Self::Output

Performs the - operation.

impl<'a> Sub<Complex<i16>> for &'a i16

type Output = Complex<i16>

The resulting type after applying the - operator.

fn sub(self, other: Complex<i16>) -> Complex<i16>

Performs the - operation.

impl Sub<Complex<i16>> for i16

type Output = Complex<i16>

The resulting type after applying the - operator.

fn sub(self, other: Complex<i16>) -> Self::Output

Performs the - operation.

impl<'a> Sub<Complex<i32>> for &'a i32

type Output = Complex<i32>

The resulting type after applying the - operator.

fn sub(self, other: Complex<i32>) -> Complex<i32>

Performs the - operation.

impl Sub<Complex<i32>> for i32

type Output = Complex<i32>

The resulting type after applying the - operator.

fn sub(self, other: Complex<i32>) -> Self::Output

Performs the - operation.

impl<'a> Sub<Complex<i64>> for &'a i64

type Output = Complex<i64>

The resulting type after applying the - operator.

fn sub(self, other: Complex<i64>) -> Complex<i64>

Performs the - operation.

impl Sub<Complex<i64>> for i64

type Output = Complex<i64>

The resulting type after applying the - operator.

fn sub(self, other: Complex<i64>) -> Self::Output

Performs the - operation.

impl<'a> Sub<