WBJEE · Maths · Complex Number
If \(z_1\) and \(z_2\) are two complex numbers satisfying the equation \(\left|\frac{z_1+z_2}{z_1-z_2}\right|=1\), then \(\frac{z_1}{z_2}\) may be
- A real positive
- B real negative
- C zero
- D purely imaginary
Answer & Solution
Correct Answer
(D) purely imaginary
Step-by-step Solution
Detailed explanation
Hint : \(\left|\frac{z_1+z_2}{z_1-z_2}\right|=1\) \(\left|z_1 / z_2+1\right|=\left|z_1 / z_2-1\right|\) Distance of \(\frac{z_1}{z_2}\) from -1 and 1 are equal So, locus of \(\frac{z_1}{z_2}\) is perpendicular bisector of line joining \((-1,0) ~\&~(1,0)\)…
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