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