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## Homework Statement

If n is an integer which leaves remainder one when divided by three, then (1+√3i)

^{n}+ (1-√3i)

^{n}equals

a) -2

^{n+1}

b) 2

^{n+1}

c) -(-2)

^{n}

d) -2

^{n}

## The Attempt at a Solution

Multiply and divide each of the two expression inside bracket by 2.

2

^{n}(cosπ/3 + isinπ/3)

^{n}+ 2

^{n}(cosπ/3-isinπ/3)

^{n}

On simplifiying, the expression equals

2

^{n}(2cosnπ/3)=2

^{n}(-1)=-2

^{n}which is same as (d)

The correct option is (c). I have no idea where I went wrong.