# Math Help - Complex Contour Question

1. ## 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
$

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.

2. Originally Posted by Haven
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
$

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.