Complex Numbers And Quadratic Equations question 56
Question: If $ \frac{2z_1}{3z_2} $ is a purely imaginary number, then $ | \frac{z_1-z_2}{z_1+z_2} | $ = [MP PET 1993]
Options:
A) 3/2
B) 1
C) 2/3
D) 4/9
Show Answer
Answer:
Correct Answer: A
Solution:
As given, let $ \frac{2z_1}{3z_2}=iy $ or $ \frac{z_1}{z_2}=\frac{3}{2}iy $ , so that $ | \frac{z_1-z_2}{z_1+z_2} |=| \frac{\frac{z_1}{z_2}-1}{\frac{z_1}{z_2}+1} |=| \frac{\frac{3}{2}iy-1}{\frac{3}{2}iy+1} |=| \frac{1-\frac{3}{2}iy}{1+\frac{3}{2}iy} |=1 $ $ { \because |z|=|\overline{z}| } $
BETA
