Complex Numbers And Quadratic Equations question 61
Question: If $ z_1 $ and $ z_2 $ are two complex numbers satisfying the equation $ | \frac{z_1+z_2}{z_1-z_2} | $ =1, then $ \frac{z_1}{z_2} $ is a number which is
Options:
A) Positive real
B) Negative real
C) Zero or purely imaginary
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Given $ | \frac{z_1+z_2}{z_1-z_2} |=1 $ Þ $ \frac{z_1+z_2}{z_1-z_2}=\cos \theta +i\sin \theta $ (say) Þ $ \frac{z_1}{z_2}=\frac{1+\cos \theta +i\sin \theta }{-1+\cos \theta +i\sin \theta }=-i\cot \frac{\theta }{2} $ which is zero, if $ \theta =n\pi (n\in I), $ and is otherwise purely imaginary.
BETA
