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Let $\gamma$ be a closed curve in U with initial point $z_0$, and let $\gamma^-$ denote its reverse curve.
Prove that $\gamma\gamma^-$ is null homotopic in U.
So I need to show that $\int_{\gamma\gamma^-}f(z)dz = 0$. How can I show this though? Not all closed curves are necessarily zero.
Prove that $\gamma\gamma^-$ is null homotopic in U.
So I need to show that $\int_{\gamma\gamma^-}f(z)dz = 0$. How can I show this though? Not all closed curves are necessarily zero.