Locus of a Complex Number Condition
Algebra · JEE Main 2015
A complex number $z$ is said to be unimodular if $|z| = 1$. Suppose $z_1$ and $z_2$ are complex numbers such that $\displaystyle\frac{z_1 - 2z_2}{2 - z_1{z_2}}$ is unimodular and $z_2$ is not unimodular. Then the point $z_1$ lies on a
Astraight line parallel to $x$-axis
Bstraight line parallel to $y$-axis
Ccircle of radius 2
Dcircle of radius $\sqrt{2}$