Question Number 146988 by mathdanisur last updated on 16/Jul/21
$${if}\:\:\:\frac{\boldsymbol{{z}}^{\mathrm{2}} \:+\:\mathrm{4}}{\boldsymbol{{z}}\:-\:\mathrm{2}\boldsymbol{{i}}}\:=\:−\mathrm{5}\:+\:\mathrm{10}\boldsymbol{{i}} \\ $$$${find}\:\:\:{Re}\left({Z}\right)\:+\:{Im}\left({Z}\right)\:=\:? \\ $$
Commented by aliibrahim1 last updated on 17/Jul/21
$${z}^{\mathrm{2}} +\mathrm{4}=\left({z}−\mathrm{2}{i}\right)\left({z}+\mathrm{2}{i}\right) \\ $$$$\frac{\left({z}−\mathrm{2}{i}\right)\left({z}+\mathrm{2}{i}\right)}{{z}−\mathrm{2}{i}}=−\mathrm{5}+\mathrm{10}{i} \\ $$$${z}+\mathrm{2}{i}=−\mathrm{5}+\mathrm{10}{i} \\ $$$${z}=−\mathrm{5}+\mathrm{8}{i} \\ $$$${Re}\left({z}\right)=−\mathrm{5} \\ $$$${Im}\left({z}\right)=\mathrm{8} \\ $$$$−\mathrm{5}+\mathrm{8}=\mathrm{3} \\ $$
Commented by mathdanisur last updated on 17/Jul/21
$${thank}\:{you}\:{Ser} \\ $$
Commented by aliibrahim1 last updated on 17/Jul/21
$${you}\:{are}\:{welcome}\: \\ $$