I have list of poles listed in a vector, poles list = {.....}. They are shown in the figure attached. To use Cauchy’s residue theorem, I would like to select only the poles of the shaded area in the figure. How can I do that in Mathematica?

complex plane with poles

  • 1
    $\begingroup$ This question is highly underspecified. What are you trying to do? Pick out the desired poles from a list? Perform a contour integral that surrounds those poles? Evaluate the residues at those poles? All we have is a drawn figure, and it's impossible to understand what exactly you want to do in Mathematica. Please edit your post by clicking the grey edit button below your post and add more information. $\endgroup$
    – march
    Commented Nov 21, 2017 at 16:40
  • $\begingroup$ Just picking the poles from a list. $\endgroup$
    – qahtah
    Commented Nov 21, 2017 at 16:47

1 Answer 1


Let's say the list is in the form of a list of pole locations (i.e., complex numbers). Call the list z. Then select those that fulfill the criteria specified by the line in the picture: those that have imaginary parts positive and also those with zero imaginary and positive real. Hence:

z = Table[i + j I, {i, -5, 5}, {j, -5, 5}] // Flatten
Select[z, Im[#] > 0 || (Im[#] == 0 && Re[#] > 0) &]
  • $\begingroup$ Thanks for your help. $\endgroup$
    – qahtah
    Commented Nov 21, 2017 at 17:15

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