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  • $\begingroup$ Can you give us values to use for A, j, h ? Also why are you solving for u and not z? If you have a list of roots then Select[{1 + I 2, 1 - I 2, 3 + I 5, 3 - I 5}, Im[#] > 0 &] will select those with positive imaginary part. $\endgroup$ Commented Jun 1, 2017 at 21:25
  • $\begingroup$ Sorry about that, my code actually has $u$ in it (I've been doing variable changes and it's hard to keep track) but I changed it to $z$ to post here since it's a question on complex numbers. I'm editing it. $A,j$ and $h$ are parameters of the problem, and I'd like my integral (and thus the residues) in terms of them. Would that be too difficult a problem to solve? And thanks for your suggestion, I'm just trying it out! $\endgroup$ Commented Jun 1, 2017 at 21:33
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    $\begingroup$ A possibility would be to replace the parameters with specific symbolic constants e.g. {E,Pi,EulerGamma}. Do the integral, by residues or otherwise, and then substitute back, This will be correct for a range of parameter values though that will have a dependency on where certain polynomials in the parameters vanish. Could do similar substitutions to handle other regions of parameter space. $\endgroup$ Commented Jun 2, 2017 at 14:36