WBJEE · Maths · Complex Number
If \(z_1, z_2\) are complex numbers such that \(\frac{2 z_1}{3 z_2}\) is a purely imaginary number, then the value of \(\left|\frac{z_1-z_2}{z_1+z_2}\right|\) is
- A \(1\)
- B \(2\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(A) \(1\)
Step-by-step Solution
Detailed explanation
Given: \(\frac{2 z_1}{3 z_2}\) is purely imaginary \(\Rightarrow \operatorname{Re}\left(\frac{z_1}{z_2}\right)=0 \Rightarrow \frac{z_1}{z_2}\) is purely imaginary Let \(\frac{z_1}{z_2}=i k\) for some real \(k\) Then \(z_1=i k z_2\) Now compute:…
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