Complex Analysis and Conformal Mapping
rational functions, exponentials, trigonometric functions, logarithms, and many more — have natural complex extensions. For example, complex polynomials p(z) = anzn+ a n−1 z n−1 + ···+ a 1 z+a0 (2.2) are complex linearcombinations (meaning thatthe coefficients akareallowed tobe complex numbers) of the basic monomial functions zk= (x+ ...
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