Using $\displaystyle z^{-1} = \frac{z*}{|z|^2}$, geometrically show how you would construct $\displaystyle z^{-1}$.

NOTE z* means the conjugate of z.

I have no idea. I know how to show it algebraically, since we'd have:

$\displaystyle \frac{1}{(a+ib)} = \frac{(a-ib)}{a^2+b^2}$

Then, multiply the left side by the complex conjugate and we get the right hand side...

How'd I show this geometrically?