Let the vertices , , , ,

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

Problem

Let the vertices

A(a)

B(b)

C(c)

D(d)

E(e)

, and

F(f)

, taken in anticlockwise order, form a regular hexagon in the Argand plane. If

a=-2

and

c=1-\sqrt{3}i

, where

i=\sqrt{-1}

, find the value of

d^2-a^2-b^2-c^2-e^2-f^2