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

$\displaystyle \frac{1}{2i}\int_C z^{*} \mathrm dz

$

Where $\displaystyle z^{*}$ 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.