angle argument of complex numbers, in radians

## Syntax

                A = angle(Z)

## Arguments

Z
  Array of real or complex numbers.

A
  Array of real numbers in (-π,π], of size(Z): the arguments (phases) of respective Z elements, in radians.

## Description

`angle(Z)` computes and returns the arguments of given complex numbers.

Special cases:

- `angle(0)` is `0`.
- For any `Z` element whose real or an imaginary of both parts is `%nan`, `angle(Z)` is `%nan`.
- For any `Z` element whose both real and imaginary parts are infinite (positive or negative), `angle(Z)` is `%nan`.

## Examples

    // Real axis
    angle([-%inf -2 -1 0 1 2 %inf])

    // Imaginary axis
    z = complex(zeros(1,7), [-%inf -2 -1 0 1 2 %inf])
    angle(z)

    // Real = Imag
    z = complex([-%inf -2 -1 0 1 2 %inf], [-%inf -2 -1 0 1 2 %inf])
    angle(z)

    // Real>0 = -Imag
    z = complex([0 1 2 %inf], [0 -1 -2 -%inf])
    angle(z)

    // Real<0 = -Imag
    z = complex(-[0 1 2 %inf], [0 1 2 %inf])
    angle(z)

    --> // Real axis
    --> angle([-%inf -2 -1 0 1 2 %inf])
     ans  =
       3.1415927   3.1415927   3.1415927   0.   0.   0.   0.

    --> // Imaginary axis
    --> z = complex(zeros(1,7),[-%inf -2 -1 0 1 2 %inf])
     z  =
       0. - Infi   0. - 2.i   0. - i     0. + 0.i   0. + i     0. + 2.i   0. + Infi
    --> angle(z)
     ans  =
      -1.5707963  -1.5707963  -1.5707963   0.   1.5707963   1.5707963   1.5707963

    --> // Real = Imag
    --> z = complex([-%inf -2 -1 0 1 2 %inf], [-%inf -2 -1 0 1 2 %inf])
     z  =
      -Inf - Infi  -2. - 2.i  -1. - i     0. + 0.i   1. + i     2. + 2.i   Inf + Infi
    --> angle(z)
     ans  =
       Nan  -2.3561945  -2.3561945   0.   0.7853982   0.7853982   Nan

    --> // Real>0 = -Imag
    --> z = complex([0 1 2 %inf], [0 -1 -2 -%inf])
     z  =
       0. + 0.i   1. - i     2. - 2.i   Inf - Infi
    --> angle(z)
     ans  =
       0.  -0.7853982  -0.7853982   Nan

    --> // Real<0 = -Imag
    --> z = complex(-[0 1 2 %inf], [0 1 2 %inf])
     z  =
       0. + 0.i  -1. + i    -2. + 2.i  -Inf + Infi
    --> angle(z)
     ans  =
       0.   2.3561945   2.3561945   Nan

## See also

- abs

## History

2023.1 `angle()` introduced.