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Homework Help: Simple complex integral

  1. Jun 8, 2006 #1

    I have a question about a complex integral. The question is about the index of a curve. This curve is defined as:

    j = j1 * j2

    with j1: r*exp(i*t) with t: [0,pi]
    and j2: [-r,r]

    This is quite simple: a half cirle followed by a line from (-r,0) through (0,0) to (r,0).
    To calculate the index Ind(a) over the curve j:

    Ind(a) = 1/(2*pi*i) * integral(dz/(z-a))

    Now the problem: I used a curve (a+r*exp(it)) to solve the half circle, this give me 1/2. But how can I calculate the index of the line from (-r,0) to (r,0)?
  2. jcsd
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