If n is a positive integer, then which of the following relations is false

i^{4 n} = 1

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i^{4 n - 1} = i

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i^{4 n + 1} = i

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i^{4 n + 2} = - 1

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Solution

The correct option is B $i^{4 n - 1} = i$
We know that $i^{2} = - 1 \Rightarrow (i^{2})^{2} = (- 1)^{2} = 1 \Rightarrow i^{4 n} = 1^{n}$ and therefore $i^{4 n - 1} = - i$

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