Square of Complex Modulus equals Complex Modulus of Square

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

Let $\cmod z$ be the modulus of $z$.

Then:
 * $\cmod {z^2} = \cmod z^2$

Proof
From Complex Modulus of Product of Complex Numbers:
 * $\cmod {z_1 z_2} = \cmod {z_1} \cmod {z_2}$

for $z_1, z_2 \in \C$.

Set $z = z_1 = z_2$ and the result follows.