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Find the smallest positive integer value...

Find the smallest positive integer value of n for which `(1+i)^n/(1-i)^(n-2)` is a real number.

A

2

B

1

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`((1+i)^(n))/((1-i)^(n-2))={(1+i)^(2)}/(1-i^(2)}^(n)(1-2i+i^(2))-(i)^(n)(-2i)=-2i^(n+1)`
This will be a real number if n+1 is an even integer is 1. Therefore, n=1.
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