So I was given a quadratic $x^4-4x^2-5$ and found the field extension $\mathbf {Q}[\sqrt {5},i] $. How do I find $[\mathbf{Q}[\sqrt {5},i] :\mathbf{Q}]$?
2026-03-27 06:17:04.1774592224
Show degree of a field extension over the rationals
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$[\Bbb Q(\sqrt5,i): \Bbb Q] = [\Bbb Q(\sqrt5):\Bbb Q][\Bbb Q(i):\Bbb Q]$ since $\Bbb Q(\sqrt5) \cap \Bbb Q(i) = \Bbb Q$.
Thus $[\Bbb Q(\sqrt5,i): \Bbb Q] = 2.2 =4$.