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Question Number 25139 by tawa tawa last updated on 05/Dec/17

$$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{real}\mathrm{and}\mathrm{the}\mathrm{imaginary}\mathrm{part}\mathrm{of}\mathrm{the}\mathrm{complex}\mathrm{number}\mathrm{z}={(-1)}^{1000003}$$

Answered by Rasheed.Sindhi last updated on 05/Dec/17

$${(-\mathrm{i})}^{1000003}={\left\{{(-\mathrm{i})}^2\right\}}^{500001}(-\mathrm{i})$$$$={(-1)}^{500001}(-\mathrm{i})=(-1)(-\mathrm{i})=\mathrm{i}$$$$=0+\mathrm{i}$$$$\mathrm{Real}\mathrm{psrt}0,\mathrm{Imaginary}\mathrm{part}1$$

Commented by tawa tawa last updated on 05/Dec/17

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

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