Possible values for a complex integral

**dudyu** · May 12th 2010, 07:37 AM

Hello,
How many possible values are there for the following integral-

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

(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 $z_i$

**shawsend** · May 12th 2010, 08:42 AM

Looks like $2^n$ to me if the poles are simple and residues do not cancel one or more of each other.

**Bruno J.** · May 12th 2010, 08:50 AM

Originally Posted by dudyu

Hello,
How many possible values are there for the following integral-

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

(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 $z_i$

Otherwise there are infinitely many possible values!

**dudyu** · May 12th 2010, 09:00 AM

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 $z_i$ . Why's that?

**shawsend** · May 12th 2010, 09:57 AM

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.

**dudyu** · May 12th 2010, 01:06 PM

Got it. Thanks very much!

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