Q. If $\frac{5z^{2}}{11z_{1}}$ is purely imaginary, then the value of $\left| \frac{2z_{1} + 3z_{2}}{2z_{1} - 3z_{2}} \right|$ is
A) 37/33
B) 2
C) 1
D) 3
Explanation
(c)
Let $\frac{5z_{2}}{11z_{1}} = iy\ \ \ \Rightarrow \ \ \frac{z_{2}}{z_{1}} = \frac{11}{5}\ iy$
Now, $\left| \frac{2z_{1} + 3z_{2}}{2z_{1} - 3z_{2}} \right| = \left| \frac{2 + 3\frac{z_{2}}{z_{1}}}{2 - 3\frac{z_{2}}{z_{1}}} \right| = \left| \frac{2 + \frac{33}{5}iy}{2 - \frac{33}{5}iy} \right| = 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.