Exponential on Complex Plane is Group Homomorphism

Theorem
Let $\left({\C, +}\right)$ be the additive group of complex numbers.

Let $\left({\C_{\ne 0}, \times}\right)$ be the multiplicative group of complex numbers.

Let $\exp: \left({\C, +}\right) \to \left({\C_{\ne 0}, \times}\right)$ be the mapping:
 * $x \mapsto \exp \left({x}\right)$

where $\exp$ is the exponential function.

Then $\exp$ is a group homomorphism.