# angle

Symbolic polar angle

## Description

example

angle(Z) computes the polar angle of the complex value Z.

## Examples

### Compute Polar Angle of Numeric Inputs

Compute the polar angles of these complex numbers. Because these numbers are not symbolic objects, you get floating-point results.

[angle(1 + i), angle(4 + pi*i), angle(Inf + Inf*i)]
ans =
0.7854    0.6658    0.7854

### Compute Polar Angle of Symbolic Inputs

Compute the polar angles of these complex numbers which are converted to symbolic objects:

[angle(sym(1) + i), angle(sym(4) + sym(pi)*i), angle(Inf + sym(Inf)*i)]
ans =
[ pi/4, atan(pi/4), pi/4]

### Compute Polar Angle of Symbolic Expressions

Compute the limits of these symbolic expressions:

syms x
limit(angle(x + x^2*i/(1 + x)), x, -Inf)
limit(angle(x + x^2*i/(1 + x)), x, Inf)
ans =
-(3*pi)/4

ans =
pi/4

### Compute Polar Angle of Array

Compute the polar angles of the elements of matrix Z:

Z = sym([sqrt(3) + 3*i, 3 + sqrt(3)*i; 1 + i, i]);
angle(Z)
ans =
[ pi/3, pi/6]
[ pi/4, pi/2]

## Input Arguments

collapse all

Input, specified as a number, vector, matrix, array, or a symbolic number, variable, expression, function.

## Tips

• Calling angle for numbers (or vectors or matrices of numbers) that are not symbolic objects invokes the MATLAB® angle function.

• If Z = 0, then angle(Z) returns 0.

## Alternatives

For real X and Y such that Z = X + Y*i, the call angle(Z) is equivalent to atan2(Y,X).

## Version History

Introduced in R2013a