Hello. Please answer the question using pen and paper. Thank you.

1. Find Laurent series about the indicated singularity for each of the following functions and name the singularity: [5] e2z z - sin z (a) (z-1)3' z = 1. (c) 73 z = 0. (e) z2 (2 - 3)21 2 = 3. (b) (z - 3) sin z+ 2' Z = -2. (d) Z (2 + 1) (2+2)' Z = -2. 2. Expand f (z) = (z+1) (z+3) in a Laurent series valid for: [5] (a) 1 3, (c) 0