NTHU OCW 程守庆教授复分析第一次期中考题

Suppose that $f$ is holomorphic in a domain and that, at every point, either mapping $f%3D0$ or $f'%3D0$ . Show that $f$ is a constant.
Evaluate the given line integral: $%5Cint%5Climits_%7B%7Cz%7C%3D2%7D%20%5Cfrac%7B4%5C%2Cdz%7D%7Bz%5E2(z%2B1)(%5Cbar%7Bz%7D%5E2-5%5Cbar%7Bz%7D%2B4)%7D$
Evaluate the given principal value integral: $%5Ctext%7BP.V.%7D%20%5Cint_%7B-%5Cinfty%7D%5E%7B%5Cinfty%7D%20%5Cfrac%7B%5Cmathrm%7Bd%7Dx%7D%7Bx%5E3%2B4x%2B5%7D$