[JEE Main 2015] z is unimodular if z 1 if z 1 2z 2 2 z 1
$z$ is unimodular if $|z|=1$. If $\dfrac{z_1-2z_2}{2-z_1\bar z_2}$ is unimodular and $z_2$ is not unimodular, then $z_1$ lies on
(a) a circle of radius $2$
(b) a circle of radius $\sqrt2$
(c) a line parallel to the $x$-axis
(d) a line parallel to the $y$-axis
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
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Correct answer: (a) a circle of radius $2$
$\left|\frac{z_1-2z_2}{2-z_1\bar z_2}\right|=1\Rightarrow|z_1-2z_2|^2=|2-z_1\bar z_2|^2$, which simplifies (using $|z_2|\ne1$) to $|z_1|^2=4$, i.e. $|z_1|=2$.
JEE Main 2015 · Complex Numbers — verified solution by the Vidaara Team.
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