Definition:Continuous Complex Function/Epsilon-Delta

Definition
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 $a \in A_1$.

$f$ is continuous at (the point) $a$ :


 * $\forall \epsilon > 0: \exists \delta > 0: \forall z \in A_1: \cmod {z - a} < \delta \implies \cmod {\map f z - \map f a} < \epsilon$