Can someone please tell me how to determine the minimal polynomial of $i+\sqrt{2}$ and $\sqrt{1+\sqrt{3}}$ over $\mathbb{Q}$ ?
My idea was to look at the iterates of these polynomials and find a linear combination of them to then get my minimal polynomial. I tried finding that relation using the recipe given to me in the previous question, but didn't quite manage it, since that contained too many points where I simply didn't knew what to do next and why to do it :(