If and are non-zero complex numbers satisfying and

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

Problem

a, b, c, a_1, b_1

and

c_1

are non-zero complex numbers satisfying

\frac{a}{a_1} + \frac{b}{b_1} + \frac{c}{c_1} = 1 + i

and

\frac{a_1}{a} + \frac{b_1}{b} + \frac{c_1}{c} = 0

, where

i = \sqrt{-1}

, the value of

\frac{a^2}{a_1^2} + \frac{b^2}{b_1^2} + \frac{c^2}{c_1^2}

is (1) 2i (2)

2+2i

(3) 2 (4) None of these