Loading [MathJax]/jax/output/HTML-CSS/jax.js
Back to the class
Homework 7 (MATH 1199 Fall 2019)
1. Draw the contour given by the formula...
(a) {z(t)=4eit0≤t≤π
(b) z(t)={t−i0≤t≤2t+(t−3)i2≤t≤3.
2. Draw the contour C and calculate the integral...
(a) ∫C1zdz,C:{z(t)=eit0≤t≤2π
(b) ∫C1z2dz,C:{z(t)=eit0≤t≤2π
(c) ∫Cz+2zdz,C:{z(t)=1+eit0≤t≤π
(d) ∫Cz2+2zdz,C:{z(t)=eit0≤t≤2π
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 n≠−1. (hint: parametrize C in the "usual way")