\begin{definition}[Definition:Inverse Tangent/Complex/Definition 2]
Let $S$ be the subset of the complex plane:
:$S = \C \setminus \set {0 + i, 0 - i}$
The '''inverse tangent''' is a multifunction defined on $S$ as:
:$\forall z \in S: \tan^{-1} \paren z := \set {\dfrac 1 {2 i} \ln \paren {\dfrac {i - z} {i + z} } + k \pi: k \in \Z}$
where $\ln$ denotes the complex natural logarithm as a multifunction.
\end{definition}