How to solve b and c

1. (12pts, 3pts each) Answer the following questions. Justify your calculation/answers and report your answers in rectangular coordinates. Note Log z is the principal branch of log z. (a) Let C be the line segment from 1 to i. Compute S. 3(Im(z) )'dz. (b) Let Ci(-2) be the circle counterclockwise with center -2 and radius 1. Find J,(-2) 23+8 Log(iz) dz. (c) Calculate the residue Resz=0 25 cos( ). (d) Find the radius of convergence of the Taylor's series of f (z) = ez (z2+1) (22_64)3 at the point 1