Fundamental theorem of algebra: Difference between revisions
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[[Image:Carl-friedrich-gauss-962c0e.jpg|frame|left|Johann Carl Friedrich Gauß (Apr 30, 1777 – Feb 23, 1855)]] | |||
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 field <math>\mathbb C</math> of complex numbers is said to be '''algebraically closed''' because it contains the roots of all its algebraic equations. | 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. | ||
Latest revision as of 05:07, 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.
