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Residues and Contour Integration Problems. Classify the singularity of f(z) at the indicated point. 1. f(z) = cot(z) at z = 0. Ans. Simple pole. Solution. When C is simple closed curve, then the complex integral is also called as a contour integral and is denoted as ∮ ( ) . us to solve certain integrals that are otherwise hard or impossible to solve. contour integration problems, the contour is sketched for you as a curveComplex Analysis, Contour Integration and Transform Theory. 1 The real parts of three analytic functions are sinxcoshy; ey2−x2 cos 2xy;. Such type of examples can be solved easily using contour integration.] Procedure for evaluation above integral: Consider given integral ∫ ( ,