Complex Numbers and Functions
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We introduced complex numbers in Sect. 1.8 of the first volume. There we just defined the numbers themselves, but did not go any further. In fact, since the introduction of complex numbers a number of centuries ago, the theory based on them has been substantially developed into an extended analysis of complex functions defined on the complex plane. The mathematical tool thus created represents an extremely powerful device for solving practical problems ranging from calculating real integrals to solving partial differential equations.