Definition:Inverse Tangent/Complex/Definition 1

Definition
Let $S$ be the subset of the complex plane:
 * $S = \C \setminus \left\{{0 + i, 0 - i}\right\}$

The inverse tangent is a multifunction defined on $S$ as:


 * $\forall z \in S: \tan^{-1} \left({z}\right) := \left\{{w \in \C: \tan \left({w}\right) = z}\right\}$

where $\tan \left({w}\right)$ is the tangent of $w$.

Also see

 * Equivalence of Definitions of Complex Inverse Tangent Function


 * Definition:Complex Arctangent