Determine the following Laurent series. a. 2 - on i. { z E C|0 v2} b. 2+2 on 2 - i. { z E C|0 1} 2 C. (2 - 1) (2 +4) on i. { z E C|0 5}. 6. (16 points) Sections 6.1-6.3 For each of the singularities of the following functions: i. find the residues ii. find the principal parts ii. classify the singularities as one of the types: removable, pole or essential. sin z2 a. 24 cosh z b. 22 z + 2 C. 22 - 3z d. zez 7. (15 points) Sections 6.4 6.6 Use the residue theorem to calculate the following integrals. dx a. I1 = 202 + 9 b. 12 = dx (2 + 1) 2 "cos 2x dx C. 13 = 202 + 4 2iyx + elir dx d. I4 = -OC 202 + 4