# Possible values for a complex integral

#### 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 closed contour that does not go through any of the points $$\displaystyle z_i$$

#### shawsend

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

ques and dudyu

#### Bruno J.

MHF Hall of Honor
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!

#### 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?

#### shawsend

MHF Hall of Honor
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

Got it. Thanks very much!