# Possible values for a complex integral

• May 12th 2010, 07:37 AM
dudyu
Possible values for a complex integral
Hello,
How many possible values are there for the following integral-

$\displaystyle \oint_{C}\frac{dz}{(z-z_1)(z-z_2)..(z-z_n)}$

(I'm guessing the answer is not n, but don't see why)

Should also add that C is a closed contour that does not go through any of the points $\displaystyle z_i$
• May 12th 2010, 08:42 AM
shawsend
Looks like $\displaystyle 2^n$ to me if the poles are simple and residues do not cancel one or more of each other.
• May 12th 2010, 08:50 AM
Bruno J.
Quote:

Originally Posted by dudyu
Hello,
How many possible values are there for the following integral-

$\displaystyle \oint_{C}\frac{dz}{(z-z_1)(z-z_2)..(z-z_n)}$

(I'm guessing the answer is not n, but don't see why)

Should also add that C is a simple closed contour that does not go through any of the points $\displaystyle z_i$

Otherwise there are infinitely many possible values!
• May 12th 2010, 09:00 AM
dudyu
Thanks for the replies.
Well, assuming poles are simple and residues don't cancel each other, I take it there are 2 possible values per point $\displaystyle z_i$ . Why's that?
• May 12th 2010, 09:57 AM
shawsend
Just start drawing circles around each combination of poles and include one circle that does not include any and keep in mind I would have gotten this one wrong as per Bruno up there. :)
• May 12th 2010, 01:06 PM
dudyu
Got it. Thanks very much!