\begin{definition}[Definition:Differentiable Mapping/Complex Function/Point]
Let $D \subset \C$ be an open set.
Let $f : D \to \C$ be a complex function.
Let $z_0 \in D$ be a point in $D$.
Then $f$ is '''complex-differentiable''' at $z_0$ {{iff}} the limit:
:$\ds \lim_{h \mathop \to 0} \frac {\map f {z_0+h} - \map f {z_0}} h$
exists as a finite number.
This limit, if it exists, is called the derivative of $f$ at $z_0$.
\end{definition}