Returns the complex argument of a complex number.

angle(*z*)

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/CSE/CE

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 $re^{i\theta}$ (or, equivalently, $r(\cos\theta+i\sin\theta)$), then $\theta$ is equal to the value of `angle(z)`, suitably reduced so that the result returned is in the interval $-\pi<\theta\leq\pi$.

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).

# Related Commands

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