## 9768 Problem# 53

Forum for the GRE subject test in mathematics.
Swimguy112
Posts: 7
Joined: Wed Aug 12, 2009 11:42 am

### 9768 Problem# 53

Hey, I was wondering if anyone managed to solve problem 53 on the practice test GR9768? The problem is:

In the complex plane, let C be the circle |z|=2 with positive (counterclockwise) orientation. Then the line integral of a scalar-valued function 1/((z-1)*(z+3)^2) over path C is

(A) 0

(B) 2*pi*i

(C) (pi*i)/2

(D) (pi*i)/8

(E) (pi*1)/16

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The answer is supposed to be (D), however after several attempts I continue to get (A).
Could someone possible show the first one or two steps of this problem? Don't worry about writing the whole thing out. Thanks!

diogenes
Posts: 73
Joined: Sun Aug 31, 2008 9:31 pm

### Re: 9768 Problem# 53

Are you using the Residue Theorem?
Notice that we have one (simple) pole at z = 1 within the circle.
So, we can say the value of the integral is 2*Pi*i*Res(f,1) = 2*Pi*i*(1/16).

Swimguy112
Posts: 7
Joined: Wed Aug 12, 2009 11:42 am

Thanks!