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Contour integral of Log(z)

  1. Mar 14, 2012 #1
    1. The problem statement, all variables and given/known data
    Find the contour integral of Log(z). The contour is defined as: x^2 + 4y^2 = 4, x>= 0, y>=0

    2. Relevant equations

    3. The attempt at a solution
    parametrize the contour as z(t) = 2cos(t) + isin(t)
    0 <= t <= pi/2
    The contour integral = ∫Log(z(t))z'(t)dt
    I am having trouble finding Log(z(t)).
    Log(z(t)) = ln|z(t)| + iArg(z(t))

    Would ln|z(t)| = ln|sqrt(1 + 3cos(t)^2)| and Arg(z(t)) = t?
  2. jcsd
  3. Mar 14, 2012 #2
    What's wrong with antiderivatives? I mean why not use the Fundamental Theorem of Calculus for this? You know the starting point of integration and the ending point so poke-a-poke right?
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