# [−][src]Struct na::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

## Methods

### `impl<T> Complex<T> where    T: Clone + Num, `[src]

#### `pub fn new(re: T, im: T) -> Complex<T>`[src]

Create a new Complex

#### `pub fn i() -> Complex<T>`[src]

Returns imaginary unit

#### `pub fn norm_sqr(&self) -> T`[src]

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) -> Complex<T>`[src]

Multiplies `self` by the scalar `t`.

#### `pub fn unscale(&self, t: T) -> Complex<T>`[src]

Divides `self` by the scalar `t`.

### `impl<T> Complex<T> where    T: Neg<Output = T> + Clone + Num, `[src]

#### `pub fn conj(&self) -> Complex<T>`[src]

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

#### `pub fn inv(&self) -> Complex<T>`[src]

Returns `1/self`

### `impl<T> Complex<T> where    T: Clone + FloatCore, `[src]

#### `pub fn is_nan(self) -> bool`[src]

Checks if the given complex number is NaN

#### `pub fn is_infinite(self) -> bool`[src]

Checks if the given complex number is infinite

#### `pub fn is_finite(self) -> bool`[src]

Checks if the given complex number is finite

#### `pub fn is_normal(self) -> bool`[src]

Checks if the given complex number is normal

## Trait Implementations

### `impl<'a, T> Add<&'a Complex<T>> for Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `+` operator.

### `impl<'a, 'b, T> Add<&'b Complex<T>> for &'a Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `+` operator.

### `impl<'a, 'b, T> Add<&'a T> for &'b Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `+` operator.

### `impl<T> Add<T> for Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `+` operator.

### `impl<'a, T> Add<&'a T> for Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `+` operator.

### `impl<'a, T> Add<T> for &'a Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `+` operator.

### `impl<T> Add<Complex<T>> for Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `+` operator.

### `impl<'a, T> Add<Complex<T>> for &'a Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `+` operator.

### `impl<T> Clone for Complex<T> where    T: Clone, `[src]

#### `default fn clone_from(&mut self, source: &Self)`1.0.0[src]

Performs copy-assignment from `source`. Read more

### `impl<T> Num for Complex<T> where    T: Clone + Num, `[src]

#### `fn from_str_radix(    s: &str,     radix: u32) -> Result<Complex<T>, <Complex<T> as Num>::FromStrRadixErr>`[src]

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

### `impl<T> Hash for Complex<T> where    T: Hash, `[src]

#### `default fn hash_slice<H>(data: &[Self], state: &mut H) where    H: Hasher, `1.3.0[src]

Feeds a slice of this type into the given [`Hasher`]. Read more

### `impl<'a, T> Rem<T> for &'a Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `%` operator.

### `impl<'a, 'b, T> Rem<&'a T> for &'b Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `%` operator.

### `impl<'a, T> Rem<&'a Complex<T>> for Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `%` operator.

### `impl<'a, T> Rem<Complex<T>> for &'a Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `%` operator.

### `impl<'a, T> Rem<&'a T> for Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `%` operator.

### `impl<T> Rem<Complex<T>> for Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `%` operator.

### `impl<'a, 'b, T> Rem<&'b Complex<T>> for &'a Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `%` operator.

### `impl<T> Rem<T> for Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `%` operator.

### `impl<'a, T> Mul<Complex<T>> for &'a Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `*` operator.

### `impl<'a, T> Mul<&'a Complex<T>> for Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `*` operator.

### `impl<'a, 'b, T> Mul<&'a T> for &'b Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `*` operator.

### `impl<'a, T> Mul<&'a T> for Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `*` operator.

### `impl<'a, 'b, T> Mul<&'b Complex<T>> for &'a Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `*` operator.

### `impl<T> Mul<Complex<T>> for Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `*` operator.

### `impl<'a, T> Mul<T> for &'a Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `*` operator.

### `impl<T> Mul<T> for Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `*` operator.

### `impl<T> Inv for Complex<T> where    T: Neg<Output = T> + Clone + Num, `[src]

#### `type Output = Complex<T>`

The result after applying the operator.

### `impl<'a, T> Inv for &'a Complex<T> where    T: Neg<Output = T> + Clone + Num, `[src]

#### `type Output = Complex<T>`

The result after applying the operator.

### `impl<T> Sub<T> for Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `-` operator.

### `impl<T> Sub<Complex<T>> for Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `-` operator.

### `impl<'a, 'b, T> Sub<&'a T> for &'b Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `-` operator.

### `impl<'a, T> Sub<&'a Complex<T>> for Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `-` operator.

### `impl<'a, 'b, T> Sub<&'b Complex<T>> for &'a Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `-` operator.

### `impl<'a, T> Sub<Complex<T>> for &'a Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `-` operator.

### `impl<'a, T> Sub<T> for &'a Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `-` operator.

### `impl<'a, T> Sub<&'a T> for Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `-` operator.

### `impl<T> Neg for Complex<T> where    T: Neg<Output = T> + Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `-` operator.

### `impl<'a, T> Neg for &'a Complex<T> where    T: Neg<Output = T> + Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `-` operator.

### `impl<T> FromStr for Complex<T> where    T: FromStr + Num + Clone, `[src]

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

The associated error which can be returned from parsing.

#### `fn from_str(s: &str) -> Result<Complex<T>, <Complex<T> as FromStr>::Err>`[src]

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

### `impl<T> Div<Complex<T>> for Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `/` operator.

### `impl<'a, T> Div<&'a T> for Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `/` operator.

### `impl<'a, 'b, T> Div<&'a T> for &'b Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `/` operator.

### `impl<T> Div<T> for Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `/` operator.

### `impl<'a, T> Div<T> for &'a Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `/` operator.

### `impl<'a, T> Div<Complex<T>> for &'a Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `/` operator.

### `impl<'a, 'b, T> Div<&'b Complex<T>> for &'a Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `/` operator.

### `impl<'a, T> Div<&'a Complex<T>> for Complex<T> where    T: Clone + Num, `[src]

#### `type Output = Complex<T>`

The resulting type after applying the `/` operator.

### `impl<N> AbstractRingCommutative<Additive, Multiplicative> for Complex<N> where    N: AbstractRingCommutative<Additive, Multiplicative> + ClosedNeg + Clone + Num, `[src]

#### `default fn prop_mul_is_commutative_approx(args: (Self, Self)) -> bool where    Self: RelativeEq<Self>, `[src]

Returns `true` if the multiplication operator is commutative for the given argument tuple. Approximate equality is used for verifications. Read more

#### `default fn prop_mul_is_commutative(args: (Self, Self)) -> bool where    Self: Eq, `[src]

Returns `true` if the multiplication operator is commutative for the given argument tuple.

### `impl<N> Module for Complex<N> where    N: RingCommutative + NumAssign, `[src]

#### `type Ring = N`

The underlying scalar field.

### `impl<N> TwoSidedInverse<Additive> for Complex<N> where    N: TwoSidedInverse<Additive>, `[src]

#### `default fn two_sided_inverse_mut(&mut self)`[src]

In-place inversion of `self`, relative to the operator `O`. Read more

### `impl<N> TwoSidedInverse<Multiplicative> for Complex<N> where    N: ClosedNeg + Clone + Num, `[src]

#### `default fn two_sided_inverse_mut(&mut self)`[src]

In-place inversion of `self`, relative to the operator `O`. Read more

### `impl<N> NormedSpace for Complex<N> where    N: RealField, `[src]

#### `type RealField = N`

The result of the norm (not necessarily the same same as the field used by this vector space).

#### `type ComplexField = N`

The field of this space must be this complex number.

### `impl<N> AbstractModule<Additive, Additive, Multiplicative> for Complex<N> where    N: AbstractRingCommutative<Additive, Multiplicative> + ClosedNeg + Num, `[src]

#### `type AbstractRing = N`

The underlying scalar field.

### `impl<N1, N2> SubsetOf<Complex<N2>> for Complex<N1> where    N2: SupersetOf<N1>, `[src]

#### `default fn from_superset(element: &T) -> Option<Self>`[src]

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more

### `impl<N> ComplexField for Complex<N> where    N: RealField, `[src]

#### `type RealField = N`

Type of the coefficients of a complex number.

#### `fn exp(self) -> Complex<N>`[src]

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

#### `fn ln(self) -> Complex<N>`[src]

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`.

#### `fn sqrt(self) -> Complex<N>`[src]

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`.

#### `fn powf(self, exp: <Complex<N> as ComplexField>::RealField) -> Complex<N>`[src]

Raises `self` to a floating point power.

#### `fn log(self, base: N) -> Complex<N>`[src]

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

#### `fn powc(self, exp: Complex<N>) -> Complex<N>`[src]

Raises `self` to a complex power.

#### `fn sin(self) -> Complex<N>`[src]

Computes the sine of `self`.

#### `fn cos(self) -> Complex<N>`[src]

Computes the cosine of `self`.

#### `fn tan(self) -> Complex<N>`[src]

Computes the tangent of `self`.

#### `fn asin(self) -> Complex<N>`[src]

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`.

#### `fn acos(self) -> Complex<N>`[src]

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`.

#### `fn atan(self) -> Complex<N>`[src]

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`.

#### `fn sinh(self) -> Complex<N>`[src]

Computes the hyperbolic sine of `self`.

#### `fn cosh(self) -> Complex<N>`[src]

Computes the hyperbolic cosine of `self`.

#### `fn tanh(self) -> Complex<N>`[src]

Computes the hyperbolic tangent of `self`.

#### `fn asinh(self) -> Complex<N>`[src]

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`.

#### `fn acosh(self) -> Complex<N>`[src]

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)) < ∞`.

#### `fn atanh(self) -> Complex<N>`[src]

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`.

#### `default fn to_polar(self) -> (Self::RealField, Self::RealField)`[src]

The polar form of this complex number: (modulus, arg)

#### `default fn to_exp(self) -> (Self::RealField, Self)`[src]

The exponential form of this complex number: (modulus, e^{i arg})

#### `default fn signum(self) -> Self`[src]

The exponential part of this complex number: `self / self.modulus()`

Cardinal sine

Cardinal cos

### `impl<N> AbstractQuasigroup<Multiplicative> for Complex<N> where    N: Num + Clone + ClosedNeg, `[src]

#### `default fn prop_inv_is_latin_square_approx(args: (Self, Self)) -> bool where    Self: RelativeEq<Self>, `[src]

Returns `true` if latin squareness holds for the given arguments. Approximate equality is used for verifications. Read more

#### `default fn prop_inv_is_latin_square(args: (Self, Self)) -> bool where    Self: Eq, `[src]

Returns `true` if latin squareness holds for the given arguments. Read more

### `impl<N> AbstractQuasigroup<Additive> for Complex<N> where    N: AbstractGroupAbelian<Additive>, `[src]

#### `default fn prop_inv_is_latin_square_approx(args: (Self, Self)) -> bool where    Self: RelativeEq<Self>, `[src]

Returns `true` if latin squareness holds for the given arguments. Approximate equality is used for verifications. Read more

#### `default fn prop_inv_is_latin_square(args: (Self, Self)) -> bool where    Self: Eq, `[src]

Returns `true` if latin squareness holds for the given arguments. Read more

### `impl<N> AbstractMagma<Multiplicative> for Complex<N> where    N: Clone + Num, `[src]

#### `default fn op(&self, O, lhs: &Self) -> Self`[src]

Performs specific operation.

### `impl<N> AbstractMagma<Additive> for Complex<N> where    N: AbstractMagma<Additive>, `[src]

#### `default fn op(&self, O, lhs: &Self) -> Self`[src]

Performs specific operation.

### `impl<N> VectorSpace for Complex<N> where    N: Field + NumAssign, `[src]

#### `type Field = N`

The underlying scalar field.

### `impl<N> Identity<Additive> for Complex<N> where    N: Identity<Additive>, `[src]

#### `default fn id(O) -> Self`[src]

Specific identity.

### `impl<N> Identity<Multiplicative> for Complex<N> where    N: Clone + Num, `[src]

#### `default fn id(O) -> Self`[src]

Specific identity.

### `impl<N> AbstractRing<Additive, Multiplicative> for Complex<N> where    N: AbstractRing<Additive, Multiplicative> + ClosedNeg + Clone + Num, `[src]

#### `default fn prop_mul_and_add_are_distributive_approx(    args: (Self, Self, Self)) -> bool where    Self: RelativeEq<Self>, `[src]

Returns `true` if the multiplication and addition operators are distributive for the given argument tuple. Approximate equality is used for verifications. Read more

#### `default fn prop_mul_and_add_are_distributive(args: (Self, Self, Self)) -> bool where    Self: Eq, `[src]

Returns `true` if the multiplication and addition operators are distributive for the given argument tuple. Read more

### `impl<N> AbstractGroupAbelian<Additive> for Complex<N> where    N: AbstractGroupAbelian<Additive>, `[src]

#### `default fn prop_is_commutative_approx(args: (Self, Self)) -> bool where    Self: RelativeEq<Self>, `[src]

Returns `true` if the operator is commutative for the given argument tuple. Approximate equality is used for verifications. Read more

#### `default fn prop_is_commutative(args: (Self, Self)) -> bool where    Self: Eq, `[src]

Returns `true` if the operator is commutative for the given argument tuple.

### `impl<N> AbstractGroupAbelian<Multiplicative> for Complex<N> where    N: Num + Clone + ClosedNeg, `[src]

#### `default fn prop_is_commutative_approx(args: (Self, Self)) -> bool where    Self: RelativeEq<Self>, `[src]

Returns `true` if the operator is commutative for the given argument tuple. Approximate equality is used for verifications. Read more

#### `default fn prop_is_commutative(args: (Self, Self)) -> bool where    Self: Eq, `[src]

Returns `true` if the operator is commutative for the given argument tuple.

### `impl<N> AbstractMonoid<Multiplicative> for Complex<N> where    N: Num + Clone + ClosedNeg, `[src]

#### `default fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> bool where    Self: RelativeEq<Self>, `[src]

Checks whether operating with the identity element is a no-op for the given argument. Approximate equality is used for verifications. Read more

#### `default fn prop_operating_identity_element_is_noop(args: (Self,)) -> bool where    Self: Eq, `[src]

Checks whether operating with the identity element is a no-op for the given argument. Read more

### `impl<N> AbstractMonoid<Additive> for Complex<N> where    N: AbstractGroupAbelian<Additive>, `[src]

#### `default fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> bool where    Self: RelativeEq<Self>, `[src]

Checks whether operating with the identity element is a no-op for the given argument. Approximate equality is used for verifications. Read more

#### `default fn prop_operating_identity_element_is_noop(args: (Self,)) -> bool where    Self: Eq, `[src]

Checks whether operating with the identity element is a no-op for the given argument. Read more

### `impl<N> AbstractSemigroup<Additive> for Complex<N> where    N: AbstractGroupAbelian<Additive>, `[src]

#### `default fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where    Self: RelativeEq<Self>, `[src]

Returns `true` if associativity holds for the given arguments. Approximate equality is used for verifications. Read more

#### `default fn prop_is_associative(args: (Self, Self, Self)) -> bool where    Self: Eq, `[src]

Returns `true` if associativity holds for the given arguments.

### `impl<N> AbstractSemigroup<Multiplicative> for Complex<N> where    N: Num + Clone + ClosedNeg, `[src]

#### `default fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where    Self: RelativeEq<Self>, `[src]

Returns `true` if associativity holds for the given arguments. Approximate equality is used for verifications. Read more

#### `default fn prop_is_associative(args: (Self, Self, Self)) -> bool where    Self: Eq, `[src]

Returns `true` if associativity holds for the given arguments.

## Blanket Implementations

### `impl<T, U> TryFrom for T where    U: Into<T>, `[src]

#### `type Error = Infallible`

The type returned in the event of a conversion error.

### `impl<T, U> TryInto for T where    U: TryFrom<T>, `[src]

#### `type Error = <U as TryFrom<T>>::Error`

The type returned in the event of a conversion error.

### `impl<T> Scalar for T where    T: Copy + PartialEq<T> + Any + Debug, `[src]

#### `default fn is<T>() -> bool where    T: Scalar, `[src]

Tests if `Self` the same as the type `T` Read more

### `impl<T> Same for T`

#### `type Output = T`

Should always be `Self`