If , then prove that lies on the bisectors of the quadrants, where…

MATHEMATICS · Subjective · CBSE · Mathematics · Complex Numbers and Quadratic Equations · Complex Numbers and Quadratic Equations

Problem

|z - i \operatorname{Re}(z)| = |z - \operatorname{Im}(z)|

, then prove that

z

lies on the bisectors of the quadrants, where

i = \sqrt{-1}