Problem

1. (10 points): Let

$$I=\oint_C \frac{y}{x^2+y^2}\,dx-\frac{x}{x^2+y^2}\,dy$$

where $C$ is a circle oriented counterclockwise. (a) Evaluate $I$ if $C$ is given by $(x-2016)^2+(y-2016)^2=1$. (b) Evaluate $I$ if $C$ is given by $x^2+y^2=1$.