Proving the Value of a Complex Integral Involving Cosecant and the Unit Circle

benjamin198
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I need help to solve this problem from Complex variables, Arthur A. Hauser, Ch. 5. pag. 122. Problem 5.42
show that ∫ csc(z)dz/z = 0
where C is the unit circle around the origin.


Solve it without using The Cauchy Integral Formula...
 

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hi benjamin198! :smile:

you need to prove ∫02π csc(eiθ) dθ = 0

perhaps there's something symmetric, or anti-symmetric, about the integrand? :wink:
 

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