Complex Modulus of Additive Inverse

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

Let $-z$ be the negative of $z$:
 * $z + \left({-z}\right) = 0$

Then:
 * $\left\vert{z}\right\vert = \left\vert{\left({-z}\right)}\right\vert$

where $\left\vert{z}\right\vert$ denotes the modulus of $z$.

Proof
Let $z = a + i b$.