\begin{definition}[Definition:Inverse Secant/Complex/Definition 1]
Let $z \in \C_{\ne 0}$ be a non-zero complex number.
The '''inverse secant of $z$''' is the multifunction defined as:
:$\map {\sec^{-1} } z := \set {w \in \C: \map \sec w = z}$
where $\map \sec w$ is the secant of $w$.
\end{definition}