Exponential Function is Continuous/Complex
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Theorem
The complex exponential function is continuous.
That is:
- $\forall z_0 \in \C: \ds \lim_{z \mathop \to z_0} \exp z = \exp z_0$
Proof
This proof depends on the differential equation definition of the exponential function.
The result follows from Complex-Differentiable Function is Continuous.
$\blacksquare$