Problem 1 0 points possible (ungraded. results hidden) Integrate the function f(2) = (z 7 32i)'2 from z = D to z = 16 + 16i along the line x = y. [4] Problem 2 0 points possible (ungraded. results hidden) Letf(z):zi+(z2] Part (a) Integrate the function f(z)along the curve C given by z = i:3+it32 from z = l + 1i to z = 64 + 16i Part (b) Integrate the same function along the line from O to 9i, then along the line from 9i to 9 + 9i, then finallyr along the line from 9 + Bite 0. Note that you are evaluating the integral on a triangular loop. Pa rt (c) Integrate the function f[z)on the circle that goes through 0! 9i, and 9 + 9i. Are the integrals in Part (in) and Part (c) equal? [5] Problem 3 0 points possible (Ungraded. results hidden) 1 Letf(z)= 2_4 Pa rt (a) Integrate the function f[z)along the curve C in the complex plane given by 1' : from x = 0.5 to x = 2 Part (b) Integrate the same function along the unit circle in the complex plane, i.e. on |z| = 1. Problem 4 0 points possible (Ungraded, results hidden) Let f (2:) = 39" Part (a) Find the integral of the function f(2:))n the circle of radius 3 centered around Din the complex plane. Part (b) 2 Now, find the integral ofthe same function on an ellipse in the complex plane given by the equation % + 5T5 = l [6]