\begin{definition}[Definition:Hyperbolic Tangent/Definition 3]
The '''hyperbolic tangent''' function is defined on the complex numbers as:
:$\tanh: X \to \C$:
:$\forall z \in X: \tanh z := \dfrac {e^{2 z} - 1} {e^{2 z} + 1}$
where:
: $X = \set {z: z \in \C, \ e^{2 z} + 1 \ne 0}$
\end{definition}