Question Number 223255 by profrey last updated on 19/Jul/25
$${Which}\:{of}\:{the}\:{following}\:{complex} \\ $$$${numbers}\:{is}\:{equivalent}\:{to}\:\frac{\mathrm{3}−\mathrm{5}{i}}{\mathrm{8}+\mathrm{2}{i}}?\left({Note}:\:{i}=\sqrt{\left.−\mathrm{1}\right)}\right. \\ $$$$\left.{A}\right)\frac{\mathrm{3}}{\mathrm{8}}−\frac{\mathrm{5}{i}}{\mathrm{2}} \\ $$$$ \\ $$$$\left.{B}\right)\frac{\mathrm{3}}{\mathrm{8}}+\frac{\mathrm{5}{i}}{\mathrm{2}} \\ $$$$\: \\ $$$$\left.{C}\right)\frac{\mathrm{7}}{\mathrm{34}}−\frac{\mathrm{23}{i}}{\mathrm{34}} \\ $$$$ \\ $$$$\left.{D}\right)\frac{\mathrm{7}}{\mathrm{34}}+\frac{\mathrm{23}{i}}{\mathrm{34}} \\ $$
Answered by Simurdiera last updated on 20/Jul/25
$$\mathrm{Respuesta}\:\mathrm{inciso}\:\left({C}\right) \\ $$
Answered by gregori last updated on 20/Jul/25
$$\:\frac{\mathrm{3}−\mathrm{5}{i}}{\mathrm{8}+\mathrm{2}{i}}\:=\:\frac{\mathrm{3}−\mathrm{5}{i}}{\mathrm{8}+\mathrm{2}{i}}\:×\:\frac{\mathrm{8}−\mathrm{2}{i}}{\mathrm{8}−\mathrm{2}{i}} \\ $$$$\:\:=\:\frac{\mathrm{24}−\mathrm{46}{i}−\mathrm{10}}{\mathrm{64}+\mathrm{4}}\:=\:\frac{\mathrm{14}−\mathrm{46}{i}}{\mathrm{68}} \\ $$$$\:\:=\:\frac{\mathrm{7}}{\mathrm{34}}−\frac{\mathrm{23}{i}}{\mathrm{34}} \\ $$