Zero (Complex Analysis)
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High Quality Content by WIKIPEDIA articles! In complex analysis, a zero of a holomorphic function f is a complex number a such that f(a) = 0.The fundamental theorem of algebra says that every nonconstant polynomial with complex coefficients has at least one zero in the complex plane. This is in contrast to the situation with real zeros: some polynomial functions with real coefficients have no real zeros. An example is f(x) = x2 + 1.An important property of the set of zeros of a holomorphic function of one variable (that is not identically zero) is that the zeros are isolated. In other words, f...
High Quality Content by WIKIPEDIA articles! In complex analysis, a zero of a holomorphic function f is a complex number a such that f(a) = 0.The fundamental theorem of algebra says that every nonconstant polynomial with complex coefficients has at least one zero in the complex plane. This is in contrast to the situation with real zeros: some polynomial functions with real coefficients have no real zeros. An example is f(x) = x2 + 1.An important property of the set of zeros of a holomorphic function of one variable (that is not identically zero) is that the zeros are isolated. In other words, for any zero of a holomorphic function there is a small disc around the zero which contains no other zeros.
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