The value of ∑ k = 1 10 sin ⁡ 2 π k 11 - i cos ⁡ 2 π k 11 is (where i = - 1 )

Question

The value of ∑ k = 1 10 sin ⁡ 2 π k 11 - i cos ⁡ 2 π k 11 is (where i = - 1 ), 1, - 1, i, - i

MARKS App · Accepted Answer

We have, ∑ k = 1 10 sin ⁡ 2 π k 11 - i cos ⁡ 2 π k 11 = ∑ k = 1 10 - i 2 sin ⁡ 2 π k 11 - i cos ⁡ 2 π k 11 = - i ∑ k = 1 10 cos ⁡ 2 π k 11 + i sin ⁡ 2 π k 11 = - i ∑ k = 1 10 e i 2 π k 11 = - i ∑ k = 0 10 e i 2 π k 11 - 1 = - i s u m o f 11 t h r o o t s o f u n i t y - 1 = - i 0 - 1 = i .

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