jee-main 2015 Q76

jee-main · India · 10apr Complex Numbers Argand & Loci Circle Equation and Properties via Complex Number Manipulation
A complex number $z$ is said to be unimodular if $|z| = 1$. Suppose $z_1$ and $z_2$ are complex numbers such that $\frac{z_1 - 2z_2}{2 - z_1\bar{z}_2}$ is unimodular and $z_2$ is not unimodular. Then the point $z_1$ lies on a:
(1) straight line parallel to $x$-axis
(2) straight line parallel to $y$-axis
(3) circle of radius 2
(4) circle of radius $\sqrt{2}$ 
A complex number $z$ is said to be unimodular if $|z| = 1$. Suppose $z_1$ and $z_2$ are complex numbers such that $\frac{z_1 - 2z_2}{2 - z_1\bar{z}_2}$ is unimodular and $z_2$ is not unimodular. Then the point $z_1$ lies on a:\\
(1) straight line parallel to $x$-axis\\
(2) straight line parallel to $y$-axis\\
(3) circle of radius 2\\
(4) circle of radius $\sqrt{2}$
Paper Questions
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