If and are the vertices of an equilateral triangle with as its circumcentre

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

Problem

z_1, z_2

and

z_3

are the vertices of an equilateral triangle with

z_0

as its circumcentre, then changing origin to

z_0

, show that

Z_1^2 + Z_2^2 + Z_3^2 = 0

, where

Z_1, Z_2, Z_3

are new complex numbers of the vertices.