On an argand diagram the points P and Q represent the numbers $z1$ and $z2$ respectively. OPQ is an equilateral triangle. Show that $(z1)^2 + (z2)^2 = z1z2$
2. Represent one number as $re^{i\varphi}$ and the other as $re^{i\varphi+i\pi/3}$ and use the fact that $e^{i\pi/3}=1+e^{i2\pi/3}$.