Suppose we have a Jordan curve , then there will exist open connected sets, the of , where this curve is the boundary between those sets.

This all means that the interior set is in the "left" of the counterclockwise rotation of the curve .

This can be summarized in a very simple sentence:

From the Gauchy-Goursat Theorem we get that if for a domain that is open and a function that is holomorphic, a Jordan Curve with its interior contained in that domain, then the line integral of that function around this Jordan Curve is zero.