If , where , and , satisfies the condition that is purely real, the set of values of…

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

Problem

\omega = \alpha + i\beta

, where

\beta \neq 0

i = \sqrt{-1}

and

z \neq 1

, satisfies the condition that

\left(\frac{\omega - \bar{\omega}z}{1 - z}\right)

is purely real, the set of values of

z

is (1)

\{z : |z| = 1\}

(2)

\{z : z = \bar{z}\}

(3)

\{z : z \neq 1\}

(4)

\{z : |z| = 1, z \neq 1\}