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The value of ...

Question

The value of $(1 - i)^{n} {(1 - \frac{1}{i})}^{n}$ is equal to

A

(- 1)^{n}

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B

1

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C

(- 2)^{n}

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D

2^{n}

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Solution

The correct option is D $2^{n}$
Given:
$(1 - i)^{n} {(1 - \frac{1}{i})}^{n} = (1 - i)^{n} {(1 - \frac{i}{i^{2}})}^{n} = (1 - i)^{n} (1 + i)^{n} (∵ i^{2} = - 1) = (1 - i^{2})^{n} = 2^{n}$

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