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Theorem name

  1. Sep 19, 2004 #1
    What is the theorem that states if [tex] \Omega [/tex] is a polynom with degree > 1 with real coefficients. If there exists a complex number [tex] z = a + bi [/tex] such that [tex] \Omega(a+bi)=0 [/tex] then [tex] \overline{z} = a - bi [/tex] is also a root of [tex] \Omega [/tex]? For [tex] \Omega(x) = x^2 + px + q [/tex] with p and q real then if a+bi is a root then a-bi is also a root if [tex] b \neq 0 [/tex], that one is easy but I don't think it's easy for degree > 2 to prove it that's why I'm search for it's name.
     
  2. jcsd
  3. Sep 19, 2004 #2

    matt grime

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    it doesn't have a name, as far as i know, and it is easy to prove. if z is a root of P, then z* is a root of P*, where * denotes conjugation, and by P*, I mean the polynomial where you replace the coeffs with their conjugates. (You understand that (uv)*=u*v*?)
     
  4. Sep 19, 2004 #3
    It does get mentioned along with FTA but i wouldn't bet on it having some special name.

    -- AI
     
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