MathVibes on Instagram: "In complex analysis, the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions over closed curves; it can often be used to compute real integrals and infinite series as well. It generalizes the Cauchy integral theorem and Cauchy's integral formula. The Residue Theorem is a powerful tool in complex analysis that simplifies evaluating complex line integrals over closed curves by relating the integral