(I think this question is acceptable for this site.)
I ask Maple to evaluate integral(1/(exp(i*t)-z),t,-π,π), and I get [if |z| = 1 then undefined else -(2*π)/z]. I understand the first part, the integrand is singular. However, for |z| ≠ 1, this is an integral of a finite continuous function over a finite closed interval, which must exist and be finite, unlike -(2*π)/0 = -∞ = ∞. Am I just very confused here, or is Maple screwing up? If the first one, how am I confused? If the second one, how should I evaluate the integral?