The points A and B represent the complex numbers $z_1$ and $z_2$ respectively on an Argand diagram, where $0.
Give geometrical constructions to find the points C and D representing $z_1+z_2$ and $z_1-z_2$ respectively.
Given that $arg(z_1-z_2)-arg(z_1+z_2)=\frac{\pi}{2}$, pprove that $|z_1|=|z_2|$.
I attached the diagram. What I need help with is proving that $|z_1|=|z_2|$.