# Exponential Function is Continuous/Complex

## Theorem

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.

$\blacksquare$