Theorem name

  • Thread starter hedlund
  • Start date
  • #1
34
0
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.
 

Answers and Replies

  • #2
matt grime
Science Advisor
Homework Helper
9,395
4
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*?)
 
  • #3
644
1
It does get mentioned along with FTA but i wouldn't bet on it having some special name.

-- AI
 

Related Threads on Theorem name

  • Last Post
Replies
4
Views
1K
Replies
2
Views
2K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
4
Views
363
Replies
6
Views
4K
  • Last Post
Replies
4
Views
2K
Replies
30
Views
1K
Replies
5
Views
2K
  • Last Post
Replies
6
Views
1K
Top