Distance between Points in Complex Plane

Theorem
Let $A$ and $B$ be points in the complex plane such that:
 * $A = \tuple {x_1, y_1}$


 * $B = \tuple {x_2, y_2}$

Then the distance between $A$ and $B$ is given by:


 * $\size {AB} = \sqrt {\paren {x_2 - x_1}^2 + \paren {y_2 - y_1}^2}$

Proof
Let $A$ and $B$ be represented by the complex numbers $z_1$ and $z_2$ respectively.

We have: