\begin{definition}[Definition:Exponential Function/Complex]
For all definitions of the '''complex exponential function''':
:The domain of $\exp$ is $\C$.
:The image of $\exp$ is $\C \setminus \set 0$, as shown in Image of Complex Exponential Function.
For $z \in \C$, the complex number $\exp z$ is called the '''exponential of $z$'''.
\end{definition}