If Z_10 and Z_2 be two complex numbers such that Z_2Z_1 is a purely imaginary number, then…

Question

If $Z_1
e0$ and $Z_2$ be two complex numbers such that $\dfrac{Z_2}{Z_1}$ is a purely imaginary number, then $\left|\dfrac{2Z_1+3Z_2}{2Z_1-3Z_2}ight|$ is equal to:

Accepted Answer

Take $Z_1=1+i$, $Z_2=1-i$ (so $\dfrac{Z_2}{Z_1}=-i$, purely imaginary):

$$\frac{2Z_1+3Z_2}{2Z_1-3Z_2}=\frac{2-3i}{2+3i}\implies \left|\frac{2Z_1+3Z_2}{2Z_1-3Z_2}\right|=\frac{|2-3i|}{|2+3i|}=1.$$

Solutions · 1