Cauchy-Goursat Theorem/Examples

Examples of Use of Cauchy-Goursat Theorem

$z^2$ over $e^{i t}$ on $\hointr 0 {2 \pi}$

Let $\map \gamma t = e^{i t}$.

Let the domain of $\gamma$ be $\hointr 0 {2 \pi}$.

Let $\map f z = z^2$.

Then:

$\ds \oint_\gamma \map f z \rd z = 0$