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Complex Numbers question

2024 · 6 Apr · Shift 2 · Q31

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JEE Main
Mathematics
Complex Numbers
2024 · 6 Apr · Shift 2 · Q31

Complex Numbers question

2024 · 6 Apr · Shift 2 · Q31

JEE MainMathematicsComplex NumbersMCQ+4 / −1

If

z_1, z_2

are two distinct complex number such that

\left|\frac{z_1-2 z_2}{\frac{1}{2}-z_1 \bar{z}_2}\right|=2

, then

A
either $z_1$ lies on a circle of radius $\frac{1}{2}$ or $z_2$ lies on a circle of radius 1.
B
$z_1$ lies on a circle of radius $\frac{1}{2}$ and $z_2$ lies on a circle of radius 1.
C
either $z_1$ lies on a circle of radius 1 or $z_2$ lies on a circle of radius $\frac{1}{2}$ .
D
both $z_1$ and $z_2$ lie on the same circle.

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