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In mathematics, the fundamental theorem of algebra states that every complex polynomial p(z) in one variable and of degree n ≥ 1 has some complex root. In other words, the field of complex numbers is algebraically closed and therefore, as for any other algebraically closed field, the equation p(z) = 0 has n roots (not necessarily distinct).

The name of the theorem is now considered a misnomer by some mathematicians, since it is an instance of analysis rather than algebra ....


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