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Residue is useful in various fields, particularly in complex analysis and number theory. For instance, in complex analysis, the residue theorem allows for the evaluation of contour integrals by relating them to residues at poles of analytic functions. In number theory, residues play a crucial role in modular arithmetic, facilitating the study of congruences and properties of integers. Additionally, residues are applied in signal processing and control theory to analyze system stability and behavior.

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4d ago

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