Question 4 (Unit B4) - 25 marks (a) Locate the singularities of the function sin* 2 and classify each singularity as a removable singularity, a pole (giving its order) or an essential singularity. (b) Find two Laurent series about 0 for the function 24 f (@) = (z+ 2)(2 - 4) one on {2 : 2| 4), giving two consecutive non-zero terms. (c) Let f (=) = z exp (i) Find the Laurent series about -i for f, giving four consecutive non-zero terms. State the anmulus of convergence of the Laurent series. (ii) Determine whether the singularity of f at -i is a removable singularity, a pole or an essential singularity. (ii) Evaluate 2 exp + 1 dz where C = (2 : |= + i) = 2}