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Question Number 132384 by Tatiane last updated on 13/Feb/21

$$i^{761+i=0}$$

Answered by MJS_new last updated on 14/Feb/21

$${\mathrm{i}}^{4n}=1$$$${\mathrm{i}}^{4n+1}=\mathrm{i}$$$${\mathrm{i}}^{4n+2}=-1$$$${\mathrm{i}}^{4n+3}=-\mathrm{i}$$$$761=4\times 190+1\Rightarrow {\mathrm{i}}^{761}=\mathrm{i}\Rightarrow {\mathrm{i}}^{76\mathrm{i}}+\mathrm{i}=2\mathrm{i}\ne 0$$

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