Complex Modulus of Reciprocal of Complex Number

Theorem
Let $z \in \C$ be a complex number such that $z \ne 0$.

Let $\left\vert{z}\right\vert$ denote the complex modulus of $z$.

Then:
 * $\left\vert{\dfrac 1 z}\right\vert = \dfrac 1 {\left\vert {z} \right\vert}$

Proof
Let $z = a + i b$.