The points A and B represent the complex numbers $\displaystyle z_1$ and $\displaystyle z_2$ respectively on an Argand diagram, where $\displaystyle 0<argz_2<argz_1<\frac{\pi}{2}$.

Give geometrical constructions to find the points C and D representing $\displaystyle z_1+z_2$ and $\displaystyle z_1-z_2$ respectively.

Given that $\displaystyle arg(z_1-z_2)-arg(z_1+z_2)=\frac{\pi}{2}$, pprove that $\displaystyle |z_1|=|z_2|$.

I attached the diagram. What I need help with is proving that $\displaystyle |z_1|=|z_2|$.

Thanks