JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Analyzing +4 | -1

The smallest positive integral value of

n

such that

{\left[ {\frac{{1 + \sin \frac{\pi }{8} + i\cos \frac{\pi }{8}}}{{1 + \sin \frac{\pi }{8} - i\cos \frac{\pi }{8}}}} \right]^n}

is purely imaginary, is equal to

View answer and explanation

Correct option: A

The correct answer is A (4) because when n=4, the expression becomes purely imaginary, satisfying the condition.

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