\begin{definition}[Definition:Cotangent/Complex Function]
Let $z \in \C$ be a complex number.
The complex function $\cot z$ is defined as:
:$\cot z = \dfrac {\cos z} {\sin z} = \dfrac 1 {\tan z}$
where:
: $\sin z$ is the sine of $z$
: $\cos z$ is the cosine of $z$
: $\tan z$ is the tangent of $z$
The definition is valid for all $z \in \C$ such that $\cos z \ne 0$.
\end{definition}