Definition:Inverse Tangent/Complex/Definition 1

Definition

Let $S$ be the subset of the complex plane:

$S = \C \setminus \set {0 + i, 0 - i}$

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

$\forall z \in S: \inv \tan z := \set {w \in \C: \map \tan w = z}$

where $\map \tan w$ is the tangent of $w$.

Also see

• Equivalence of Definitions of Complex Inverse Tangent Function

• Definition:Complex Arctangent