I suppose this might fall under the heading of Pre-Calc, but since I got it out of a book on Complex Analysis I thought I'd put it here.

The problem is this:

(where $\displaystyle z_1$ and $\displaystyle z_2$ are complex numbers.)Prove the identity:

$\displaystyle |z_1 + z_2| ^2 + |z_1 - z^2|^2 = 2(|z_1|^2 + |z_2|^2)$

and interpret it geometrically.

I was able to easily prove the identity. But what is the geometric interpretation of it?

-Dan