Cauchy Integral Formula

Theorem
Let $f \left({z}\right)$ be an analytic function on and within a closed contour $C$.

Let $z_0$ be any point within $C$.

Then:


 * $\displaystyle \int_C \frac {f \left({z}\right)} {z - z_0} \ \mathrm d z = 2 \pi i f \left({z}\right)$