A complex number z is said to be unimodular i | vedclass

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(D) Given $\left|\frac{z_1 - 2z_2}{2 - z_1 \overline{z_2}}\right| = 1$.This implies $|z_1 - 2z_2|^2 = |2 - z_1 \overline{z_2}|^2$.Using the property $

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circle of radius $2$

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(D) Given $\left|\frac{z_1 - 2z_2}{2 - z_1 \overline{z_2}}ight| = 1$.This implies $|z_1 - 2z_2|^2 = |2 - z_1 \overline{z_2}|^2$.Using the property $|w|^2 = w \overline{w}$,we have:$(z_1 - 2z_2)(\overline{z_1} - 2\overline{z_2}) = (2 - z_1 \overline{z_2})(2 - \overline{z_1} z_2)$.Expanding both sides:$z_1 \overline{z_1} - 2z_1 \overline{z_2} - 2z_2 \overline{z_1} + 4z_2 \overline{z_2} = 4 - 2\overline{z_1} z_2 - 2z_1 \overline{z_2} + z_1 \overline{z_1} z_2 \overline{z_2}$.Simplifying the equation:$|z_1|^2 + 4|z_2|^2 = 4 + |z_1|^2 |z_2|^2$.Rearranging the terms:$|z_1|^2 - |z_1|^2 |z_2|^2 + 4|z_2|^2 - 4 = 0$.$|z_1|^2(1 - |z_2|^2) - 4(1 - |z_2|^2) = 0$.$(|z_1|^2 - 4)(1 - |z_2|^2) = 0$.Since it is given that $z_2$ is not unimodular,$|z_2| 
eq 1$,so $1 - |z_2|^2 
eq 0$.Therefore,$|z_1|^2 = 4$,which means $|z_1| = 2$.This represents a circle of radius $2$ centered at the origin.

$A$ complex number $z$ is said to be unimodular if $|z| = 1$. Suppose $z_1$ and $z_2$ are complex numbers such that $\frac{z_1 - 2z_2}{2 - z_1 \overline{z_2}}$ is unimodular and $z_2$ is not unimodular. Then the point $z_1$ lies on a:

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