The angle( Command

Command Summary

Returns the complex argument of a complex number.

Command Syntax


Menu Location


  1. MATH to access the math menu.
  2. RIGHT, RIGHT to access the CPX (complex) submenu
  3. 4 to select angle(, or use arrows.

Calculator Compatibility


Token Size

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+iy 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.


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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