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Question about complex integrals!

  1. Jul 30, 2011 #1
    1. The problem statement, all variables and given/known data

    Hey people got a question here about complex integration, not really sure how to do it so hope someone out there could help me!

    Evaluate the complex integrals

    ∫ c { (zbar)^2 +1 } dz........and........∫ c { zcos(z^2) - ie^2z }

    where c is the contour joining 0 to 2i along
    (i) the line segment parametrized by z(t) = 2it, t∈{0,1}
    (ii) the semicircle parametrized by z(t) = i + e^it, t∈{-pi/2, pi/2}



    2. Relevant equations



    3. The attempt at a solution
    I know we have to sub the parameterization in for z, but now that theres a line and semicircle im confused! Didnt have a great prof for this subject, so im hopin some other people could help me out
     
  2. jcsd
  3. Aug 1, 2011 #2

    lanedance

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    hi liamH

    as you are given the parameterisaton, why not try substituting it into the inetrgal, then the integration should become a simple single variable integral. Remember you will have to account for the dz as well.
     
  4. Aug 2, 2011 #3
    Ok so for the first integral and the line segment....

    int from 0 to 1 {(2it bar) ^ 2 +1} (2i) dz

    i worked this out and the answer i got was -2/3 i?

    is this right?

    and so for the semicircle the integral wil be

    int from -pi/2 to pi/2 {(-1 + e^it bar) ^2 + 1 (e^it) } ?
     
  5. Aug 3, 2011 #4

    lanedance

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    first one looks correct - probably easier if you show you working and I can check it rather than me doing the whole integral as well
     
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