Fundamental theorem of algebra

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The fundamental theorem of algebra states that
every non-constant single-variable polynomial with complex coefficients has
at least one complex root.

This includes polynomials with real coefficients, since every real number is
a complex number with its imaginary part equal to zero.

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In spite of its name, there is no purely algebraic proof of the theorem,
since any proof must use some form of the analytic completeness of the real numbers,
which is not an algebraic concept.[1]
Additionally, it is not fundamental for modern algebra;

its name was given at a time when algebra was synonymous with theory of equations.