Thread: Minimal Polynomials

Hi

I am wondering how to find the minimal polynomial of 2+\sqrt{i} over \mathbb{Q}.

I have got it to x^{4}-2x^{2}+9 but I don't know how to shaw that this is irreducible!

Thanks

Originally Posted by Kirsty

Hi

I am wondering how to find the minimal polynomial of 2+\sqrt{i} over \mathbb{Q}.

I have got it to x^{4}-2x^{2}+9 but I don't know how to shaw that this is irreducible!

Thanks

I don't know from where did you get that polynomial. I got:

, and this polynomial is irreducible by Eisenstein's criterium with after carrying on the transformation

Tonio

Oops,

I actually meant \sqrt{2}+i.

Sorry