Question

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. $\frac{37}{33}$
• B. $2$
• C. 1
• D. $3$
• E. $\frac{33}{37}$

Answer 1

Answer: (C)

Since, $\frac{5z_2}{11z_1}=iy$ (say) or $\frac{z_2}{z_1}=\frac{11}{5}iy$
Now, $\left|\frac{2z_1+3z_2}{2z_1-3z_2}\right|=\frac{\left|2+3\frac{z_2}{z_1}\right|}{\left|2-3\frac{z_2}{z_1}\right|}$
$=\frac{|2+\frac{33}{5}iy|}{|2-\frac{33}{5}iy|}=1$