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Algebra of Complex Numbers

If n is an od...

Question

If $n$ is an odd integer, $i = \sqrt{- 1}$ , then $(1 + i)^{6 n} + (1 - i)^{6 n}$ is equal to

A

0

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B

2

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C

- 2

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D

1

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Solution

The correct option is A $0$
As, $(1 + i)^{6 n} + (1 - i)^{6 n} = [(1 + i)^{2}]^{3 n} + [(1 - i)^{2}]^{3 n}$
$= (2 i)^{3 n} + (- 2 i)^{3 n}$ , as $n$ is odd
$= (2 i)^{3 n} - (2 i)^{3 n}$
$= 0$

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Algebra of Complex Numbers

Standard XII Mathematics

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