\begin{definition}[Definition:Inverse Tangent/Complex/Arctangent]
The principal branch of the complex inverse tangent function is defined as:
:$\map \arctan z := \dfrac 1 {2 i} \, \map \Ln {\dfrac {i - z} {i + z} }$
where $\Ln$ denotes the principal branch of the complex natural logarithm.
\end{definition}