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## Homework Statement

Prove that the integral of a complex exponential over an integer number of periods is zero.

## Homework Equations

[itex] \int_{0}^{T_{0}}e^{j (2\pi /T_{0}) kt} dt = 0 , k = integer[/itex]

## The Attempt at a Solution

I am never sure how to work a proof. In this case, i can see that it would be true but not sure how you go about "proving" it. That the area from 0 to 1/2 T0 would zero out the area from 1/2 T0 to T0. Can someone point me to a good example on how to work this type of proof? or help me through this one?

[itex]\frac{1}{e^{j(2\pi /T_{0})k}}e^{j(2\pi /T_{0})kt} \mid ^{0}_{T_{0}}[/itex]