Square of Complex Modulus equals Complex Modulus of Square

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

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

Then:
 * $\left\vert{z^2}\right\vert = \left\vert{z}\right\vert^2$

Proof
From Complex Modulus of Product of Complex Numbers:
 * $\left\vert{z_1 z_2}\right\vert = \left\vert{z_1}\right\vert \cdot \left\vert{z_2}\right\vert$

for $z_1, z_2 \in \C$.

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