\begin{definition}[Definition:Inverse Cotangent/Complex/Definition 1]
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 $w$.
\end{definition}