Computes the angle of a complex number or a set of complex numbers.

**angle(***Expr1***)** → *expression*

**angle(***List1***)** → *list*

**angle(***Matrix1***)** → *matrix*

The **angle(** command computes the angle of a complex number, which corresponds to the rotation of a vector whose length is equivalent to the **abs(** of the number. The angle is returned in degrees, gradians, or radians, depending on the mode the calculator is in.

```
Degree mode
:angle(1+i) = 45
Radian mode
:angle(1+i) = π/4
```

**angle(** can also return the angles for a list or matrix of complex numbers, returning the outputs in a list or matrix respectively. **angle(** will attempt to return a closed-form expression for the value rather than a decimal expression when utilizing the CAS, and can also return a symbolic evaluation of an angle.

`:angle(z) = π(sign(z)-1)/2`

# Formulas

The general formula for the angle of complex number *x+iy* is given by

Often denoted as θ, the angle of a complex number is used in its polar representation

(2)where *r* is the absolute value of the number.