JEE Mains · Maths · STD 11 - 4.1 complex nubers
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 1 or \(z_2\) lies on a circle of radius \(\frac{1}{2}\)
- B either \(z_1\) lies on a circle of radius \(\frac{1}{2}\) or \(z_2\) lies on a circle of radius \(1\) .
- C \(z_1\) lies on a circle of radius \(\frac{1}{2}\) and \(z_2\) lies on a circle of radius \(1\) .
- D both \(z_1\) and \(z_2\) lie on the same circle.
Answer & Solution
Correct Answer
(A) either \(z_1\) lies on a circle of radius 1 or \(z_2\) lies on a circle of radius \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\( \frac{z_1-2 z_2}{\frac{1}{2}-z_1 \bar{z}_2} \times \frac{\bar{z}_1-2 \bar{z}_2}{\frac{1}{2}-\bar{z}_1 z_2}=4 \) \( \left|z_1\right|^2 2 z_1 \bar{z}_2-2 \bar{z}_1 z_2+4\left|z_2\right|^2 \)…
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