Modulus of Complex Number equals its Distance from Origin

Theorem
The modulus of a complex number equals its distance from the origin on the complex plane.

Proof
Let $z = x + y i$ be a complex number and $O = 0 + 0 i$ be the origin on the complex plane.

We have its modulus:

and its distance from the origin on the complex plane:

The two are seen to be equal.