Hi all, how do I apply contour integral $I =\oint z^ndz$ where $n\in \mathbb{N}$ to solve the above diagram??
Thanks for helping everyone..
2026-04-06 20:43:35.1775508215
how to calculate contour integral for semi circle as shown
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Let $z:[0,1]\rightarrow \mathbb C,\ z (t)=1/2 e^{2\pi i t} -1/2$, be the parameterization of the curve $\gamma $. Then $\int _ \gamma z^n dz=\displaystyle \int _0 ^1 z (t)^n z'(t)dt$. Nevertheless, z^n has an entire primitive, thus integral depends only on extremal points.