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Question

If n is an integer and
(1+i3)n+(1i3)n=2n+1cosθ then θ is equal to

A
nπ3
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B
nπ2
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C
nπ4
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D
nπ6
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Solution

The correct option is A nπ3
2n(12+i32)n+2n(12i32)n
=2n(cosπ3+isinπ3)n+2n(cosπ3isinπ3)n
=2n(cosnπ3+isinnπ3+cosnπ3isinnπ3)
=2n+1cosnπ3
θ=nπ3

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