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Question

Find the value of 1 + α + α2 + α3 +.............. αn1. If αk = cos2πkn+isin2πkn,

K = 0,1,2,..........n-1


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Solution

1 + α + α2 + α3 +................... αn1

Sum of the GP = 1(1an)1a

When k =n

Given αn = cos2πkn+isin2nkn = 1

Sum of the GP = 1(11)1a = 0


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