Residue Theorem

Step 1: The integral involves a rational function in and is taken over a unit circle. To solve it, we can use the residue theorem to compute the integral by identifying the poles inside the unit circle.
Step 2: The poles of the integrand occur where the denominators are zero. These are the points where , and where and .
Step 3: After identifying the poles and applying the residue theorem, we find that the correct values for are when and when , and the corresponding answer options are (A) and (C).