If , where is a complex number, the value of (z + 1 z )^2 + (z^2 + 1 z^2 )^2 + (z^3 +…

MATHEMATICS · Single correct · CBSE · Mathematics · Complex Numbers and Quadratic Equations · Complex Numbers and Quadratic Equations

Problem

z^2 + z + 1 = 0

, where

z

is a complex number, the value of

\left(z + \frac{1}{z}\right)^2 + \left(z^2 + \frac{1}{z^2}\right)^2 + \left(z^3 + \frac{1}{z^3}\right)^2 + \dots + \left(z^6 + \frac{1}{z^6}\right)^2

is (1) 18 (2) 54 (3) 6 (4) 12