Field Norm of Complex Number is Multiplicative Function

Theorem
Let $\C$ denote the set of complex numbers.

Let $N: \C \to \R_{\ge 0}$ denote the field norm on complex numbers:
 * $\forall z \in \C: \map N z = \cmod z^2$

where $\cmod z$ denotes the complex modulus of $z$.

Then $N$ is a multiplicative function on $\C$.

Proof
So $N$ is a multiplicative function by definition.