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426:{\displaystyle {\sqrt{1}}={\begin{cases}1\\-{\frac {1}{2}}+{\frac {\sqrt {3}}{2}}i\\-{\frac {1}{2}}-{\frac {\sqrt {3}}{2}}i\end{cases}}}
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This article is about the conjugation between the roots of a polynomial. For other uses, see
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526:{\displaystyle \left(x+{\frac {1}{2}}\right)^{2}+{\frac {3}{4}}=x^{2}+x+1.}
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257:. The equivalence of the two definitions is one of the starting points of
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is specified, one can take the conjugates in some relatively small field
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can be extended to an isomorphism of the splitting fields of
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itself is included in the set of conjugates of
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214:. Conjugate elements are commonly called
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758:In summary, the conjugate elements of
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73:"Conjugate element" field theory
62:adding citations to reliable sources
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846:David S. Dummit, Richard M. Foote,
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675:. Conversely any conjugate
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866:"Conjugate Elements"
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890:Field (mathematics)
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266:complex conjugation
247:field automorphisms
863:Weisstein, Eric W.
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114:December 2010
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138:mathematics
29:Conjugation
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537:Properties
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216:conjugates
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84:newspapers
871:MathWorld
807:Kronecker
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624:Aut(
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