Question

If:\[\arg \left({z1 + z2 \over z1-z2}\right) = {\pi \over 2}\]
Show that:\[|z1| = |z2|\]

Answer 1

\[\arg\left(\frac{z_1 + z_2}{z_1-z_2}\right) = \frac\pi2 \implies \frac{z_1 +z_2}{z_1 -z_2} = \tan \frac{\pi}2 \implies z_1 =z_2 \]