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Basic Complex Analysis<1. Explain Cauchy's Theorem and its significance in complex analysis. Provide a detailed proof of the theorem.<Example: Consider the function f(z) = 1/z, where z is a complex variableexcluding the origin. Show that the integral of f(z) over a simple closed curve C not passing through the origin is zero.

Basic Complex Analysis<1. Explain Cauchy's Theorem and its significance in complex analysis. Provide a detailed proof of the theorem.<Example: Consider the function f(z) = 1/z,

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