Property	Value
Hex Value	`$BB28`
Categories	Catalog > A Math > Complex
Localizations	FR: `argument(`

`angle(`

Overview

Returns the polar angle of a complex number or list of complex numbers.

Availability: Token available everywhere.

Syntax

angle(value)

Arguments

Name	Type	Optional
value	complex\|complex[]

Location

math, CMPLX, 4:angle(

Description

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).

abs(
conj(
real(
imag(
R►Pθ(

Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, Myles_Zadok, thornahawk, Trenly.

History

Calculator	OS Version	Description
TI-83	0.01013	Added

Last update: September 30, 2023 15:38:51
Created: February 23, 2023 23:15:01

Authors: Adrien Bertrand

angle(