1. The problem statement, all variables and given/known data What is the integral of e-1/z around a unit circle centered at z = 0? 2. Relevant equations - 3. The attempt at a solution The Laurent expansion of this function gives : 1 - 1/z + 1/(2 z^2) - 1/(3! z^3) + . . . . . The residue of the pole inside is -1. So the integral should be = -2πi Is this right? Also, aren't there infinitely many poles or infinitely high order of the pole at z = 0?