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Question

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

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 B nπ3
(1+i3)n+(1i3)4=2n+1cosθ
2n(eiπ/3)n+2n(e1π/3)n=2n+1cosθ
einπ/3+einπ/3=2cosθ
cosnπ3+isinnπ3+cosnπ3isinnπ3=2cosθ
2cosnπ3=2cosθ
nπ3=θ
Hence, the answer is nπ3.


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