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Complex analysis - area inside a simple closed curve

  1. May 3, 2006 #1
    Let C be a simple closed curve. Show that the area enclosed by C is given by 1/2i * integral of conjugate of z over the curve C with respect to z.

    the hint says: use polar coordinates

    i can prove it for a circle, but i am not sure how to extend it to prove it for any given closed curve
  2. jcsd
  3. May 3, 2006 #2


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    How would you express the enclosed by an arbitrary closed curve as a double integral? Can you apply Green's theorem to turn this into a single integral over C?
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