For real variables, the definition of polynomials (linear combinations of powers) stems from the definitions of elementary algebraic operations. Since for complex variables the same algebraic rules hold, also for them the polynomial can be defined and, grouping together the terms with and without the coefficient i, we can always express them as P (z) = u (x, y) + iv (x, y), where u, v are real functions of the real variables x, y. © 2008 Birkhäuser Verlag AG.

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