Exponential Function is Superfunction

Theorem
The function $f : \C \to \C$, defined as:
 * $\map f z = c^z$

is a superfunction for any complex number $c$.

Proof
Define $h: \C \to \C$ by $\map h z = z \times c$.

Then:

Thus $\map f z = c^z$ is a superfunction and $\map h z = z \times c$ is the corresponding transfer function.