# 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 $w$.