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= Complex
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An <ordered pair> of two <real numbers> with the complex addition and multiplication defined.

Forms both a:
* <division algebra> if thought of <\R^2> with complex multiplication as the bilinear map of the <algebra over a field>[algebra]
* <field (mathematics)>


Complex number

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Kind of extends the <complex numbers>.

Some facts that make them stand out:
* one of the only three real <associative> <division algebras> in addition to the <real numbers> and <complex numbers>, according to the <classification of associative real division algebras>
* the simplest non-<commutative> <division algebra>. Contrast for example with <complex numbers> where multiplication is <commutative>


Quaternion

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An <algebra over a field> where <division> exists.


Ciro Santilli @cirosantilli 37

 Incoming links: Division algebra