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Complex Numbers

If n ∈ Z, the...

Question

If $n \in Z,$ then $(- \sqrt{- 1})^{4 n + 3}$ equals

A

- i

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B

1

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C

- 1

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D

i

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Solution

The correct option is D $i$
$(- \sqrt{- 1})^{4 n + 3} = (- i)^{4 n + 3}$
$= (- i)^{4 n} \times (- i)^{3} = ((- i)^{4})^{n} \times (- 1)^{3} \times i^{3} = 1 \times - 1 \times (- i) = i$

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Complex Numbers

Standard XII Mathematics

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