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I still can not explain why summation of $exp (iy)$ is equal to zero? why the summation of adding vector is equal to zero?

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closed as unclear what you're asking by Kyle Kanos, John Rennie, stafusa, Jon Custer, coconut Jan 11 '18 at 18:00

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Summing or integrating over a set closed under $y\mapsto\pi+y$ gives $0$, because this mapping multiplies $e^{iy}$ by $-1$.

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