WBJEE · Maths · Complex Number
If \(\frac{z-1}{z+1}\) is purely imaginary, then
- A \(|z|=\frac{1}{2}\)
- B \(|z|=1\)
- C \(|z|=2\)
- D \(|z|=3\)
Answer & Solution
Correct Answer
(B) \(|z|=1\)
Step-by-step Solution
Detailed explanation
Let \(\omega=\frac{z-1}{z+1}\) Then, using componendo and dividendo, we get \[ \begin{array}{l} \quad z=\frac{1+\omega}{1-\omega} \\ \Rightarrow \quad|z|=\left|\frac{\omega+1}{\omega-1}\right| \\ \Rightarrow \quad|z|=1 \\ \Rightarrow \quad|\omega+1|=|\omega-1| \end{array} \] Let…
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