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
*********************
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!
9768 Problem# 53
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).
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).