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Complex numbers turned out to be a fantastic tool, not only for solving equations but also for simplifying the mathematics of classical physics—the physics developed up until the 20th century.
JAN BÜTHE, A METHOD FOR PROVING THE COMPLETENESS OF A LIST OF ZEROS OF CERTAIN L-FUNCTIONS, Mathematics of Computation, Vol. 84, No. 295 (SEPTEMBER 2015), pp. 2413-2431 ...