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Math Help - Complex Contour Question

  1. #1
    Member Haven's Avatar
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    Complex Contour Question

    Let C be a positively oriented simple close contour. Show the area of region enclosed by C can be written as:

    \frac{1}{2i}\int_C z^{*} \mathrm dz<br />

    Where z^{*} is the conjugate of z.

    I have no idea where to start on this problem. I was thinking maybe countour deformation, but i have no idea how to get the area.
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  2. #2
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    Quote Originally Posted by Haven View Post
    Let C be a positively oriented simple close contour. Show the area of region enclosed by C can be written as:

    \frac{1}{2i}\int_C z^{*} \mathrm dz<br />

    Where z^{*} is the conjugate of z.

    I have no idea where to start on this problem. I was thinking maybe countour deformation, but i have no idea how to get the area.
    This should get you started.


    z=x+iy \implies \bar{z} =x-iy and

    dz=dx+idy

    Write out the integral and use Green's theorem.
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