Question Number 22434 by gopikrishnan005@gmail.com last updated on 18/Oct/17
$$\boldsymbol{\mathrm{I}}\mathrm{m}\left(\mathrm{2z}+\mathrm{1}\right)/\left(\mathrm{iz}−\mathrm{1}\right)=\mathrm{2} \\ $$
Answered by ajfour last updated on 18/Oct/17
$$\mathrm{2}{z}+\mathrm{1}=\mathrm{2}{iz}−\mathrm{2} \\ $$$$\mathrm{2}{x}+\mathrm{2}{iy}+\mathrm{1}=\mathrm{2}{ix}−\mathrm{2}{y}−\mathrm{2} \\ $$$$\Rightarrow\:\:\:\:\mathrm{2}{x}+\mathrm{2}{y}=−\mathrm{3}\:\:\:{and} \\ $$$$\:\:\:\:\:\:\:\:\:{x}={y} \\ $$$${so}\:\:\boldsymbol{{z}}=−\frac{\mathrm{3}}{\mathrm{4}}\left(\mathrm{1}+\boldsymbol{{i}}\right)\:. \\ $$