PROBLEM 4: 5z + 22 g (z) = z2 - 4 and the Contour C as given in PROBLEM 3. A B A. Write g(z) as g(z) = z - 2 z + 2 Determine A and B. Show work. What are the value of residues forg(z). Answer: B. Use Cauchy's integral Formula to determine o g(z)dz. Show all steps C Answer: Real Part = [ ]n Imaginary Part = [ ]n B. Note that g(z) = 5z + 22 f1(z) _$2(2) Determine fi(z)and z2 - 4 z -2 z+2' f2(z) in the form of two all steps different fracions. Show all steps Answers: f (z) = f2 (z ) = Which is analytic at z = +2? f, (z) or f2 (z)? Answer: Which is analytic at z = -2? f (z) or f, (z)? Answer: C. Use Results in B and Cauchy's integral Formula to determine% g(z)dz. Show all steps. C Answer: Real Part = | T Imaginary Part = | | D. Compare results in Problem 3 part D and Problem 3 parts B and C. 9z% + 30z + 60 _ _ E. Use poles for f(x) = m Then use Partial Fraction method to find residues for f(x). Note there are 2 real poles p; and p, and 2 imaginary poles p; and p, . 9z2 + 30z + 60 A B C D + + HINT: - = [ = =9 7=p, T2=p, T7=ps T7-ms Now find values for A,B,C,D.Show all steps