TS EAMCET · Maths · Complex Number
If \(z_1, z_2\) are two complex numbers satisfying \(\left|\frac{z_1-3 z_2}{3-z_1 \bar{z}_2}\right|=1,\left|z_1\right| \neq 3\), then \(\left|z_2\right|\) is equal to
- A \(1\)
- B \(2\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(A) \(1\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Given that }\left|\frac{z_1-3 z_2}{3-z_1 \bar{z}_2}\right|=1,\left|z_1\right| \neq 3 \\ & \Rightarrow\left|z_1-3 z_2\right|=\left|3-z_1 \bar{z}_2\right| \quad\left[\because\left|\frac{z_1}{z_2}\right|=\frac{\left|z_1\right|}{\left|z_2\right|}\right] \\…
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