3. For each of the following, construct a function f, analytic in the plane except for isolated singularities, that satisfies the given conditions. (a) f has a zero of order 2 at z = i and a pole of order 5 at z = 2-3i. (b) f has a simple zero at z = 0 and an essential singularity at z = 1. (c) f has a removable singularity at z = essential singularity at z = i. 0, a pole of order 6 at z = 1, and an (d) f has a pole of order 2 at z = 1 + i and essential singularities at z = z = 1. O and