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Question Number 190275 by aye786naing last updated on 30/Mar/23

$$\mathrm{Find}\mathrm{the}\mathrm{value}\mathrm{of}{\mathrm{i}}^{\mathrm{n}}\mathrm{for}\mathrm{every}\mathrm{positive}$$$$\mathrm{integer}\mathrm{n},\mathrm{where}{\mathrm{i}}^2=-1,{\mathrm{i}}^3={\mathrm{i}}^2\mathrm{i},{\mathrm{i}}^4={\mathrm{i}}^2{\mathrm{i}}^2,etc.$$

Answered by Frix last updated on 31/Mar/23

$$k\in \mathbb{N}:{\mathrm{i}}^n=\{\begin{array}{l}1;n=4k\\ \mathrm{i};n=4k+1\\ -1;n=4k+2\\ -\mathrm{i};n=4k+3\end{array}$$

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