Question Number 207271 by hardmath last updated on 10/May/24
$$\mathrm{arg}\:\left(\:\frac{\mathrm{2}\:−\:\boldsymbol{\mathrm{i}}}{\boldsymbol{\mathrm{i}}}\:\right)\:=\:\mathrm{2} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{Imz}\:+\:\mathrm{Rez}\:=\:? \\ $$
Answered by A5T last updated on 10/May/24
$$\frac{\mathrm{2}−{i}}{{i}}=\frac{{i}\left(\mathrm{2}−{i}\right)}{{i}^{\mathrm{2}} }=\frac{\mathrm{2}{i}+\mathrm{1}}{−\mathrm{1}}=−\mathrm{1}−\mathrm{2}{i} \\ $$$$\Rightarrow{Imz}+{Rez}=−\mathrm{1}+\left(−\mathrm{2}\right)=−\mathrm{3} \\ $$
Commented by hardmath last updated on 10/May/24
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{dear}\:\mathrm{professor} \\ $$