# Struct num::complex::Complex [−] [src]

```pub struct Complex<T> {
pub re: T,
pub im: T,
}```

A complex number in Cartesian form.

## Fields

 `re` Real portion of the complex number `im` Imaginary portion of the complex number

## Methods

### `impl<T> Complex<T> where T: Clone + Num`

#### `fn new(re: T, im: T) -> Complex<T>`

Create a new Complex

#### `fn i() -> Complex<T>`

Returns imaginary unit

#### `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`.

#### `fn scale(&self, t: T) -> Complex<T>`

Multiplies `self` by the scalar `t`.

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

Divides `self` by the scalar `t`.

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

#### `fn conj(&self) -> Complex<T>`

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

#### `fn inv(&self) -> Complex<T>`

Returns `1/self`

### `impl<T> Complex<T> where T: Clone + Float`

Calculate |self|

#### `fn arg(&self) -> T`

Calculate the principal Arg of self.

#### `fn to_polar(&self) -> (T, T)`

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

#### `fn from_polar(r: &T, theta: &T) -> Complex<T>`

Convert a polar representation into a complex number.

#### `fn exp(&self) -> Complex<T>`

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

#### `fn ln(&self) -> Complex<T>`

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<T>`

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 sin(&self) -> Complex<T>`

Computes the sine of `self`.

#### `fn cos(&self) -> Complex<T>`

Computes the cosine of `self`.

#### `fn tan(&self) -> Complex<T>`

Computes the tangent of `self`.

#### `fn asin(&self) -> Complex<T>`

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<T>`

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<T>`

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<T>`

Computes the hyperbolic sine of `self`.

#### `fn cosh(&self) -> Complex<T>`

Computes the hyperbolic cosine of `self`.

#### `fn tanh(&self) -> Complex<T>`

Computes the hyperbolic tangent of `self`.

#### `fn asinh(&self) -> Complex<T>`

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<T>`

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<T>`

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`.

#### `fn is_nan(self) -> bool`

Checks if the given complex number is NaN

#### `fn is_infinite(self) -> bool`

Checks if the given complex number is infinite

#### `fn is_finite(self) -> bool`

Checks if the given complex number is finite

#### `fn is_normal(self) -> bool`

Checks if the given complex number is normal