I am trying to show that $\int_{C_r}\frac{1}{z^3-8}dz=0$ where $C_r$ is the circle of radius $r > 2$ centered at $0$. I have been given a hint to use the fact that $|\int_{C_r}\frac{1}{z^3-8}dz|\leq \max(|\frac{1}{z^3-8}|)(\operatorname{length}(C_r))$. I know the length of $C_r$ but how do you find the maximum of the function?
2026-04-11 08:51:37.1775897497
Finding the maximum value of a complex function
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