Due Monday in class
1. Let $C$ be the contour of $|z|=10$. Compute the following integrals.
(1) $$\oint_C \frac{1}{1+z^2} dz $$
(2) (the result for this one is not zero.) $$\oint_C \frac{z}{1+z^2} dz $$
(3) $$\oint_C \frac{z^2}{1+z^4} dz $$
Apply methods 1,2,3 to the above problems (each method need to be used once)
2. Consider the multivalued function $f(z) = \sqrt{z}$, sketch the motion of the values of $f(z)$ as $z$ moves the following curves
3. Consider the multivalued function $f(z) = \sqrt{z(z-1)}$, sketch the motion of the values of $f(z)$ as $z$ moves the following curves: $z$ along the circle of radius 10, centered at $0$.