Properties of Complex Exponential Function

Theorem
Let $z \in \C$ be a complex number.

Let $\exp z$ be the exponential of $z$.

Then:

Exponent of Sum

 * $\forall z_1, z_2 \in \C: \exp \left({z_1 + z_2}\right) = \left({\exp z_1}\right) \left({\exp z_2}\right)$

Exponential Function is Continuous

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