Exponential Function is Continuous/Complex

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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.

$\blacksquare$