Answer:
[tex]if \: {i}^{k} = 1. \: \iff\:then \: k = 0 .\\ if \: {i}^{k} = i. \: \iff\: then \: k = 1. \\ if \: {i}^{k} = - 1. \: \iff\: then \: k = 0 \: and \:i = - 1 . \\ if \: {i}^{k} = - i. \: \iff \:then \: k = 1 \: and \: i = - i.[/tex]
Step-by-step explanation:
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