I'm studying a little of Complex Analysis and I have seen that I can use the integrals of complex functions as integrals of differential forms in $\mathbb{R}^n.$ For example: Cauchy Theorem for complex analytic functions is a consequence of the fact that a closed differential form on a simply connected set is exact.

My question is : Are there other famous theorem of Complex Analysis that I can prove with the theory of differential forms in Euclidean space?


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