Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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:

    e^i(z+3)

    when converted to complex. The denominator will be factored into

    (z-2i)(z+2i)

    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

    e^(i(2i+3)/(4i)

    It follows that

    J=e^(-2+3i)*Pi

    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:

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Cauchy Residual Theorem
  1. PRESS Residuals (Replies: 1)

  2. Quadratic Residues (Replies: 3)

Loading...