1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook