Question Number 132384 by Tatiane last updated on 13/Feb/21
$${i}^{\mathrm{761}+{i}=\mathrm{0}} \\ $$
Answered by MJS_new last updated on 14/Feb/21
$$\mathrm{i}^{\mathrm{4}{n}} =\mathrm{1} \\ $$$$\mathrm{i}^{\mathrm{4}{n}+\mathrm{1}} =\mathrm{i} \\ $$$$\mathrm{i}^{\mathrm{4}{n}+\mathrm{2}} =−\mathrm{1} \\ $$$$\mathrm{i}^{\mathrm{4}{n}+\mathrm{3}} =−\mathrm{i} \\ $$$$\mathrm{761}=\mathrm{4}×\mathrm{190}+\mathrm{1}\:\Rightarrow\:\mathrm{i}^{\mathrm{761}} =\mathrm{i}\:\Rightarrow\:\mathrm{i}^{\mathrm{76i}} +\mathrm{i}=\mathrm{2i}\neq\mathrm{0} \\ $$