Question

If $\frac{2z_1}{3z_2}$ is a purely imaginary number, then $\left|\frac{z_1-z_2}{z_1+z_2}\right|$ =
[MP PET 1993]

• A. 3/2
• B. 1
• C. 2/3
• D. 4/9

Answer 1

The correct option is B

1

As given, let $\frac{2z_1}{3z_2}=iyor\frac{z_1}{z_2}=\frac{3}{2}iy,$ so that
$\left|\frac{z_1-z_2}{z_1+z_2}\right|=\left|\frac{\frac{z_1}{z_2}-1}{\frac{z_1}{z_2}+1}\right|=\left|\frac{\frac{3}{2}iy-1}{\frac{3}{2}iy+1}\right|=\left|\frac{1-\frac{3}{2}iy}{1+\frac{3}{2}iy}\right|=1\because |z|=|\overline{z}|$