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Cauchy’s Theorem: The Heart of Complex Analysis Complex analysis is a branch of mathematics that studies complex numbers and functions. In this field, Cauchy’s theorem holds central importance. The theorem determines the value of the integral along a closed curve in the complex plane. It is particularly significant for analytic functions and is widely used in many areas of complex analysis. Statement of the Theorem Cauchy’s theorem can be briefly stated as follows: If the function f(z) is analyt