\begin{definition}[Definition:Inverse Hyperbolic Secant/Complex/Principal Branch]
The principal branch of the complex inverse hyperbolic secant function is defined as:
:$\forall z \in \C: \map \Arsech z := \map \Ln {\dfrac {1 + \sqrt {1 - z^2} } z}$
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}