If n is a positive integer, then (1+i) ^ n + (1-i) ^ n is equal t… - Vidyadip

MCQ

If n is a positive integer, then ${{(1+i)}^{n}}+{{(1-i)}^{n}}$ is equal to [Orissa JEE 2003]

A
${{(\sqrt{2})}^{n-2}}\cos \left( \frac{n\pi }{4} \right)$
B
${{(\sqrt{2})}^{n-2}}\sin \left( \frac{n\pi }{4} \right)$
✓
${{(\sqrt{2})}^{n+2}}\cos \left( \frac{n\pi }{4} \right)$
D
${{(\sqrt{2})}^{n+2}}\sin \left( \frac{n\pi }{4} \right)$

✓

Answer

Correct option: C.

${{(\sqrt{2})}^{n+2}}\cos \left( \frac{n\pi }{4} \right)$

C

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