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Cauchy Residual Theorem

  1. Apr 12, 2013 #1
    Alright so I posted a picture asking the exact question.

    Here is my best attempt...

    According to my professor's terrible notes, the numerator can magically turn into the form:


    when converted to complex. The denominator will be factored into


    but the function is only holomorphic at z=2i so only (z+2i) can be used.

    From there the Res(f,2i)=g(2i) which is equal to what I believe is something like


    It follows that


    and sovling for the real part gives me an incorrect answer.

    I might be missing some steps but I'm going off a theorem and it's really hard to relate to this problem. Help me PLEASE!

    Attached Files:

  2. jcsd
  3. Apr 22, 2013 #2
    Is it 0.00477463?
  4. Apr 22, 2013 #3
    This is $$\frac{\sin (3)}{4 e^2}$$

    Let me know if this is the answer. I can explain how i got it.
  5. Apr 23, 2013 #4
    I finally calculated the answer... it turned out to be -0.2

    See the picture if you're interested

    Attached Files:

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