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Complex Contour Integral

  1. Aug 10, 2014 #1
    Hi I'm really not sure how to start this question. I could do it if it was in terms of z but I'm not sure if trying to change the variable using z = x + iy is correct. If anyone could suggest a method I'd appreciate it.

    ∫(x3 - iy2)dz

    along the path z= [itex]\gamma(t)[/itex] = t + it3, 0≤t≤1

  2. jcsd
  3. Aug 10, 2014 #2


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    Homework Helper

    I think it's safe to assume that [itex]z = x + iy[/itex] if nothing to the contrary is given.

    You have [itex]z = \gamma(t)[/itex] so [itex]dz = \gamma'(t)\,dt[/itex] and [itex]x[/itex] and [itex]y[/itex] are respectively the real and imaginary parts of [itex]\gamma(t)[/itex].
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