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Homework 7 (MATH 1199 Fall 2019)
1. Draw the contour given by the formula...
(a) {z(t)=4eit0tπ
(b) z(t)={ti0t2t+(t3)i2t3.

2. Draw the contour C and calculate the integral...
(a) C1zdz,C:{z(t)=eit0t2π
(b) C1z2dz,C:{z(t)=eit0t2π
(c) Cz+2zdz,C:{z(t)=1+eit0tπ
(d) Cz2+2zdz,C:{z(t)=eit0t2π

3. Let C be the boundary of the square with vertices at the points 0, 1, 1+i, and i oriented counterclockwise. Calculate Cπexp(π¯z)dz. (hint: break C into four parts, parametrize each separately, and add up in the integrals over each part)

4. Let C be the unit circle. Calculate Czndz, when n1. (hint: parametrize C in the "usual way")