A complex number z is said to be unimodular

Question:

A complex number $z$ is said to be unimodular if $|z|=1$. Suppose $z_{1}$ and $z_{2}$ are complex numbers such that $\frac{z_{1}-2 z_{2}}{2-z_{1} \bar{z}_{2}}$ is unimodular and $z_{2}$ is not unimodular. Then the point $z_{1}$ lies on a :

  1.  circle of radius 2

  2. circle of radius $\sqrt{2}$

  3.  straight line parallel to x-axis

  4.  straight line parallel to y-axis


Correct Option: 1

Solution:

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