I understand b and c now and how we came about finding them.
For a, I have found the singularities to be +/- sqrt(2*i*pi*n) but I am having trouble showing that these are poles of order 2. Any thoughts?
Can you show that z = 0 is a pole of order 2? There is a useful theorem in the second paragraph here: http://mathworld.wolfram.com/Pole.html (I'm sure the theorem is also in your class notes and textbook).