\begin{definition}[Definition:Inverse Secant/Complex/Arcsecant]
The principal branch of the complex inverse secant function is defined as:
:$\forall z \in \C_{\ne 0}: \map \arcsec z := \dfrac 1 i \, \map \Ln {\dfrac {1 + \sqrt {1 - z^2} } z}$
where:
:$\Ln$ denotes the principal branch of the complex natural logarithm
:$\sqrt {1 - z^2}$ denotes the principal square root of $1 - z^2$.
\end{definition}