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Question

If α=cos8π11+isin8π11 then Re(α+α2+α3+α4+α5) equals

A
0
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B
12
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C
12
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D
None of these
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Solution

The correct option is B 12
Given : α=cos8π11+isin8π11
α11=cos8π+isin8π=1
10n=0αn=1α111α=0 (sum of 11th roots of unity)
Now Re(z)=z+¯z2=sum of 11 roots of unity12=1/2

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