Fundamental theorem of algebra: Difference between revisions
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The [[fundamental theorem of algebra]] holds that every algebraic equation with coefficients in the complex numbers is solvable in the complex numbers, and has as many roots as its degree, or highest power of the unknown in any term, when the roots are counted with their multiplicity. | The [[fundamental theorem of algebra]] holds that every algebraic equation with coefficients in the complex numbers is solvable in the complex numbers, and has as many roots as its degree, or highest power of the unknown in any term, when the roots are counted with their multiplicity. | ||
The | The field <math>\mathbb C</math> of complex numbers is said to be '''algebraically closed''' because it contains the roots of all its algebraic equations. | ||
Revision as of 04:51, 27 December 2024
The fundamental theorem of algebra holds that every algebraic equation with coefficients in the complex numbers is solvable in the complex numbers, and has as many roots as its degree, or highest power of the unknown in any term, when the roots are counted with their multiplicity.
The field of complex numbers is said to be algebraically closed because it contains the roots of all its algebraic equations.
