Question Number 204583 by hardmath last updated on 22/Feb/24
$$\mathrm{For}\:\:\:\mathrm{z}\:=\:\mathrm{a}\:−\:\mathrm{bi} \\ $$$$\mathrm{If}\:\:\:\left(\mid\mathrm{z}\mid\:−\:\mathrm{z}\right)\centerdot\left(\mid\mathrm{z}\mid\:+\:\overline {\mathrm{z}}\right)\:=\:\mathrm{4bi} \\ $$$$\mathrm{Find}\:\:\:\mid\mathrm{z}\mid\:=\:? \\ $$
Answered by A5T last updated on 22/Feb/24
$$\left(\mid{z}\mid−{z}\right)\left(\mid{z}\mid+\overset{−} {{z}}\right)=\mid{z}\mid^{\mathrm{2}} +\overset{−} {{z}}\mid{z}\mid−{z}\mid{z}\mid−{z}\overset{−} {{z}} \\ $$$$=\mid{z}\mid\left(\overset{−} {{z}}−{z}\right)=\mathrm{4}{bi}\Rightarrow\mid{z}\mid=\frac{\mathrm{4}{bi}}{{a}+{bi}−\left({a}−{bi}\right)}=\mathrm{2} \\ $$