GW approximation: Difference between revisions

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{{About|binomial conjugates in algebra||Conjugate (disambiguation)}}
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In [[algebra]], a '''conjugate''' is a [[binomial]] formed by negating the second term of a binomial. The conjugate of {{nowrap|''x'' + ''y''}} is {{nowrap|''x'' − ''y''}}, where ''x'' and ''y'' are [[real number]]s. If ''y'' is [[imaginary number|imaginary]], the process is termed [[complex conjugation]]: the [[complex conjugate]] of {{nowrap|''a'' + ''bi''}} is {{nowrap|''a'' − ''bi''}}, where ''a'' and ''b'' are real.
 
== Differences of squares ==
 
{{main|Difference of two squares}}
In a [[commutative ring]], an expression of the form
 
:<math> a^2-b^2 </math>
 
can be factored to give
 
:<math> (a+b)(a-b) </math>
 
where one factor is the conjugate of the other. This can be useful when trying to [[Rationalisation (mathematics)|rationalize]] a denominator containing radicals (√).
 
==See also==
*[[Conjugate element (field theory)]]
 
==External links==
*[http://www.mathwords.com/r/rationalizing_the_denominator.htm Rationalizing the Denominator] from Mathwords.com
*[http://www.blc.edu/fac/rbuelow/common/glossarya-m.htm#conjugate Math glossary] from Bethany Lutheran College
 
[[Category:Algebra]]

Latest revision as of 18:15, 21 November 2014

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