\begin{definition}[Definition:Continuous Complex Function]
As the complex plane is a metric space, the same definition of continuity applies to complex functions as to metric spaces.
Let $A_1, A_2 \subseteq \C$ be subsets of the complex plane.
Let $f: A_1 \to A_2$ be a complex function from $A_1$ to $A_2$.
Let $a \in A_1$.
\end{definition}