\begin{definition}[Definition:Inverse Cosine/Complex/Arccosine]
The principal branch of the complex inverse cosine function is defined as:
:$\map \arccos z = \dfrac 1 i \map \Ln {z + \sqrt {z^2 - 1} }$
where:
:$\Ln$ denotes the principal branch of the complex natural logarithm
:$\sqrt {z^2 - 1}$ denotes the principal square root of $z^2 - 1$.
\end{definition}