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Complex Integration

  1. Jan 18, 2009 #1
    1. The problem statement, all variables and given/known data

    Evaluate the following intergral:

    2. Relevant equations

    Intergral from gamma of (y)dz, where gamma is the union of the line segments joining 0 to i and then i to i+2

    3. The attempt at a solution

    I have no idea how to do this!
  2. jcsd
  3. Jan 18, 2009 #2


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    Hi kmeado07! :smile:

    (have a gamma: Γ :wink:)

    Γ is an L-shaped path …

    just integrate along each bit of it separately.

    (but what is y? :confused:)
  4. Jan 18, 2009 #3


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    Presumably, if you are expected to do a problem like this, you know something about path integrals. The line from 0 to i, in the complex plane, can be written as z= (1+i)t where t ranges from 0 to 1. The line from i to i+ 2 can be written as z= (1+ t)+ i where, again, t ranges from 0 to 1. Do those two integrals separately with z replace by those and dz by (1+i)dt in the first integral and by dt in the second.

    Unfortunately, you see to have forgotten to say what the integrand, y(z), is!
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