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I'm trying to work out the integral of 1/z over the path (0, -i) to (-i, a) to (a, i) to (0, i) for a any real number greater than 0. I'm having trouble trying to determine what to do at z=0 since the integral doesn't exist here. Any ideas as far as how to push forward? My impression is that I'll have to exclude the pole at z=0 using z=ρ*exp[iθ] and taking the limit as ρ goes to 0 which will give me a closed contour. Presumably I'd have to calculate the residue as well, but I want to make sure I have this done rigorously. Would I have to use the principal value as well?

Many thanks,

jmcelve2

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# Integral of 1/z using different paths

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