Definition:Inverse Cotangent/Complex/Definition 1

Definition

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

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

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

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

where $\cot \left({w}\right)$ is the cotangent of $w$.

Also see

• Equivalence of Definitions of Complex Inverse Cotangent Function

• Definition:Complex Arccotangent