# Theorem name

1. Sep 19, 2004

### hedlund

What is the theorem that states if $$\Omega$$ is a polynom with degree > 1 with real coefficients. If there exists a complex number $$z = a + bi$$ such that $$\Omega(a+bi)=0$$ then $$\overline{z} = a - bi$$ is also a root of $$\Omega$$? For $$\Omega(x) = x^2 + px + q$$ with p and q real then if a+bi is a root then a-bi is also a root if $$b \neq 0$$, 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. Sep 19, 2004

### matt grime

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. Sep 19, 2004

### TenaliRaman

It does get mentioned along with FTA but i wouldn't bet on it having some special name.

-- AI