Mathematics - Complex Number Question with Solution | TestHub

Let $z_1=1+i$ and $z_2=1-i$ $\frac{z_2}{z_1}=\frac{1-i}{1+i}=\frac{(1-i)(1-i)}{(1+i)(1-i)}=-i$ $\frac{2z_1+3z_2}{2z_1-3z_2}=\frac{2+3\left(\frac{z_2}{z_1}\right)}{2-3\left(\frac{z_2}{z_1}\right)}=\frac{2-3i}{2+3i}$ $\left|\frac{2z_1+3z_2}{2z_1-3z_2}\right|=\left|\frac{2-3i}{2+3i}\right|=\left|\frac{2-3i}{2+3i}\right|$ $\left[\because \left|\frac{z_1}{z_2}\right|=\frac{|z_1|}{|z_2|}\right]$ $=\frac{\sqrt{4+9}}{\sqrt{4+9}}=1$