Complex Modulus of Additive Inverse

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

Let $-z$ be the negative of $z$:
 * $z + \paren {-z} = 0$

Then:
 * $\cmod z = \cmod {\paren {-z} }$

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

Proof
Let $z = a + i b$.