Question Number 25139 by tawa tawa last updated on 05/Dec/17
$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{real}\:\mathrm{and}\:\mathrm{the}\:\mathrm{imaginary}\:\mathrm{part}\:\mathrm{of}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{number}\:\:\:\mathrm{z}\:=\:\left(−\:\mathrm{1}\right)^{\mathrm{1000003}} \\ $$
Answered by Rasheed.Sindhi last updated on 05/Dec/17
$$\left(−\mathrm{i}\right)^{\mathrm{1000003}} =\left\{\left(−\mathrm{i}\right)^{\mathrm{2}} \right\}^{\mathrm{500001}} \left(−\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\:\:=\left(−\mathrm{1}\right)^{\mathrm{500001}} \left(−\mathrm{i}\right)=\left(−\mathrm{1}\right)\left(−\mathrm{i}\right)=\mathrm{i} \\ $$$$\:\:\:\:\:\:\:=\mathrm{0}+\mathrm{i} \\ $$$$\mathrm{Real}\:\mathrm{psrt}\:\mathrm{0}\:,\:\mathrm{Imaginary}\:\mathrm{part}\:\mathrm{1} \\ $$
Commented by tawa tawa last updated on 05/Dec/17
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$