is there anybody there who is interested in complex calculus?

Is the theorem right?

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When you integrate f on a closed loop, you may or may not get 0 as the total integral. It depends a lot on what f is, and what the loop is. If f has an anti-derivative on the loop, then the integral is guaranteed to be 0 by the fundamental theorem of calculus. If f is analytic on the loop and inside the loop, then Cauchy's theorem guarantees that the integral is 0. In all other cases it is very unlikely that the integral vanishes completely.

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z=2exp(

[email protected])

f(z)

[email protected] then the antiderivative is exist is 1/z and by calculation the integral yields "2pi*i". But according to the theorem above shouldn't it be 0.

Where am I wrong?