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i-761-i-0-




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

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