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
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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
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