\begin{definition}[Definition:Inverse Hyperbolic Cosine/Complex/Definition 1]
The '''inverse hyperbolic cosine''' is a multifunction defined as:
:$\forall z \in \C: \map {\cosh^{-1} } z := \set {w \in \C: z = \map \cosh w}$
where $\map \cosh w$ is the hyperbolic cosine function.
\end{definition}