Complex Modulus of Reciprocal of Complex Number

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

Let $\cmod z$ denote the complex modulus of $z$.

Then:
 * $\cmod {\dfrac 1 z} = \dfrac 1 {\cmod z}$

Proof
Let $z = a + i b$.