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

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$i^{4 n} = 1$

$i^{4 n - 1} = - i$

$i^{4 n + 1} = i$

$i^{- 4 n} = 1$

answer is B.

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Detailed Solution

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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