complex integration

Complex integration is a mathematical technique used to evaluate integrals of complex functions, which are functions that involve complex numbers. Just like how we can find areas under curves in real-number calculus, complex integration helps calculate similar properties in the realm of complex numbers. It often uses the concept of paths or contours in the complex plane. A key result of complex integration is Cauchy's Integral Theorem, which shows that the integral of a function around a closed loop is zero if the function is holomorphic (smooth) within that loop, revealing deep connections between calculus and complex analysis.