Thank you for reporting, we will resolve it shortly
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
Complex Numbers and Quadratic Equations
Solution:
Let $\frac{5z_{2}}{11z_{1}}=ki$,
where $k$ is any real constant
or $\frac{z_{2}}{z_{1}}=k' i\,\,$ [where $k' =\frac{11}{5} k]\quad...\left(i\right)$
$\therefore \, \left|\frac{2z_{1}+3z_{2}}{2z_{1}-3z_{2}}\right|$
$=\left|\frac{z_{1}\left(2+\frac{3z_{2}}{z_{1}}\right)}{z_{1}\left(2-\frac{3z_{2}}{z_{1}}\right)}\right|$
$=\left|\frac{2+3k' i}{2-3k' i}\right|$
$=1$