Exponential Function is Continuous/Complex

Theorem
The complex exponential function is continuous.

That is:
 * $\forall z_0 \in \C: \displaystyle \lim_{z \mathop \to z_0} \ \exp z = \exp z_0$

Proof
This proof depends on the differential equation definition of the exponential function.

The result follows from Complex-Differentiable Function is Continuous.