Math Help - conjugates

1. conjugates

Find the conjugates in $\mathbb{C}$ of $\sqrt{1+\sqrt{2}}$ over $\mathbb{Q}(\sqrt{2})$.

So $\text{irr}\left(\sqrt{1+\sqrt{2}}, \mathbb{Q}(\sqrt{2})\right) = x^2-\left(\sqrt{1+\sqrt{2}}\right)$.

Thus the conjugate is $-\sqrt{1+\sqrt{2}}$.

This is correct?

2. Originally Posted by Sampras
Find the conjugates in $\mathbb{C}$ of $\sqrt{1+\sqrt{2}}$ over $\mathbb{Q}(\sqrt{2})$.

So $\text{irr}\left(\sqrt{1+\sqrt{2}}, \mathbb{Q}(\sqrt{2})\right) = x^2-\left(\sqrt{1+\sqrt{2}}\right)$.

Thus the conjugate is $-\sqrt{1+\sqrt{2}}$.

This is correct?

I suppose you meant $\text{irr}\left(\sqrt{1+\sqrt{2}}, \mathbb{Q}(\sqrt{2})\right) = x^2-\left(1+\sqrt{2}\right)$, and then yes: the one you write is the conjugate.

Tonio