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Residue Calculus question

  1. Apr 19, 2010 #1
    1. The problem statement, all variables and given/known data
    25f36ae.jpg

    3. The attempt at a solution
    So there are poles at: z=[tex]\pm2[/tex] and at z= -1 of order 4. Right?

    My query is, when evaluating these poles (using the residue theorem), is it right that for (i) Z = 1/2, no residues lie in that contour?
    for (iii), do all residues lie in the contour?
     
  2. jcsd
  3. Apr 19, 2010 #2

    Dick

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    Right about the poles, but for the rest, are you just guessing? Why don't you draw a graph? No, I don't think the triangle in iii) includes all poles.
     
  4. Apr 19, 2010 #3
    ^^I wasn't sure how to determine whether a pole is inside a specified contour but my tutor suggested drawing a graph, which i have been doing, in which case shouldn't (i) have no poles in the contour? As for (iii) then, would Z=+2, and Z=-1 lie in the contour?
     
  5. Apr 19, 2010 #4

    Dick

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    Your tutor is wise. Yes, i) contains no poles and iii) contains z=(-1) and z=2.
     
  6. Apr 19, 2010 #5
    ^^Thanks :)
     
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