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# angle

P = angle(Z)

## Description

P = angle(Z) returns the phase angles, in radians, for each element of complex array Z. The angles lie between ±π.

For complex Z, the magnitude R and phase angle theta are given by

R = abs(Z)
theta = angle(Z)

and the statement

Z = R.*exp(i*theta)

converts back to the original complex Z.

## Examples

collapse all

Create a matrix of complex values and compute the phase angle of each element.

Z = [1 - 1i   2 + 1i   3 - 1i   4 + 1i
1 + 2i   2 - 2i   3 + 2i   4 - 2i
1 - 3i   2 + 3i   3 - 3i   4 + 3i
1 + 4i   2 - 4i   3 + 4i   4 - 4i];

P = angle(Z)
P = 4×4

-0.7854    0.4636   -0.3218    0.2450
1.1071   -0.7854    0.5880   -0.4636
-1.2490    0.9828   -0.7854    0.6435
1.3258   -1.1071    0.9273   -0.7854

## Algorithms

The angle function takes a complex number z = x + iy and calculates atan2(y,x) to find the angle formed in the xy-plane between the positive x-axis and a ray from the origin to the point (x,y). This phase angle is also the imaginary part of the complex logarithm, since

$\begin{array}{l}z=r{e}^{i\theta }\\ \mathrm{log}\left(z\right)=\mathrm{log}\left(r\right)+i\theta \text{\hspace{0.17em}}.\end{array}$