Compute integral of:
Integral over C of 1/z dz
where C is the unit circle centered at some point z.
Hi. Here's something fun to check your knowledge about contour integrals: pin the center of the unit circle at the point 2i. Now, drop it straight through the singular point of at the origin until the center rests at -2i. Now, how does the value of the integral change as the circle falls?