I'm solving some exercises about fields and am trying to find the inverse for $a_1 + \sqrt{2}b_1$, i.e. $\frac{1}{a_1 + \sqrt{2}b_1}$. This means I need to split the fraction into something of the form $x_1 + \sqrt{2}x_2$ but I can't seem to remember how to do such a basic thing! Can anyone help me out?
2026-04-07 19:26:30.1775589990
Basic question about fractions
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Hint: $\displaystyle \frac{1}{a_1+\sqrt{2} b_1}= \frac{a_1- \sqrt{2}b_1}{(a_1+\sqrt{2}b_1)(a_1- \sqrt{2}b_1)}$.
It is the same idea that for complex numbers.