# TI-BASIC:Angle

**Command Summary**

Returns the complex argument of a complex number.

**Command Syntax**

angle(*z*)

**Menu Location**

Press:

- MATH to access the Math menu.
- RIGHT, RIGHT to access the CPX (complex) submenu
- 4 to select angle(, or use arrows.

TI-83/84/+/SE

2 bytes

angle(*z*) returns the complex argument (also known as the polar angle) of the complex number *z*. If *z* is represented as *x*+i*y* where *x* and *y* are both real, angle(*z*) returns R►Pθ(*x*,*y*) (which is equivalent to tanֿ¹(*y*/*x*) if x is nonzero). Also works on a list of complex numbers.

angle(3+4i) .927295218 R►Pθ(3,4) .927295218

When writing a complex number *z* in the form <math>re^{i\theta}</math> (or, equivalently, <math>r(\cos\theta+i\sin\theta)</math>), then <math>\theta</math> is equal to the value of angle(*z*), suitably reduced so that the result returned is in the interval <math>-\pi<\theta\leq\pi</math>.

The angle( command also works on Matrices, though not in any useful way: angle([A] will return a matrix of the same size as [A], but with all elements 0. If you plan to use this, **don't**: 0[A] does the same thing, but is smaller and not as questionable (because this behavior is clearly unintentional on TI's part, and may be changed in an OS update).