A complex number z is said to be unimodular if | z | = 1. Suppose z₁ and z₂ are complex numbers such that (z₁ - 2z₂)/(2 - z₁ z₂) is unimodular and z₂ is not unimodular. Then the point z₁ lies on a:

(C) straight line parallel to x-axis

(D) straight line parallel to y-axis.

Complex Numbers and Quadratic Equations: JEE Main 2015 Mathematics question

JEE Main 2015 · Session, Shift 1 · Q3251

JEE Main 2015Session, Shift 1MathematicsHardComplex Numbers and Quadratic Equations264× since 2002

A complex number z is said to be unimodular if

\,\left| z \right| = 1

. Suppose

{z_1}

and

{z_2}

are complex numbers such that

{{{z_1} - 2{z_2}} \over {2 - {z_1}\overline {{z_2}} }}

is unimodular and

{z_2}

is not unimodular. Then the point

{z_1}

lies on a :