Main Content

# angle

Symbolic polar angle

## Syntax

``angle(Z)``

## 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)`.

## See Also

Introduced in R2013a

## Support

#### Mathematical Modeling with Symbolic Math Toolbox

Get examples and videos