query: Let $w\in\mathbb{C}$ be a primitive 10th root of unity. What is $[\mathbb{Q}(w):\mathbb{Q}]$?
positive_passages.docid: 24919
positive_passages.text: $\mathbb{Q}(\zeta_{10}) $ degree of field extension over $\mathbb{Q}$
negative_passages.docid: 68458
negative_passages.text: Roots of unity and large expression
negative_passages.docid: 82262
negative_passages.text: minimal polynomial of nth root of 2 over $\mathbb Q$
negative_passages.docid: 30601
negative_passages.text: Number of $60$th primitive roots of $-1$
negative_passages.docid: 120940
negative_passages.text: An irreducible polynomial in a subfield of $\mathbb{C}$ has no multiple roots in $\mathbb{C}$
negative_passages.docid: 19884
negative_passages.text: The units of $\mathbb Z_4[x]$
negative_passages.docid: 51314
negative_passages.text: How to prove that a complex number is not a root of unity?
negative_passages.docid: 128575
negative_passages.text: Elementary proof that $3$ is a primitive root of a Fermat prime?
negative_passages.docid: 50823
negative_passages.text: Primitive polynomials
negative_passages.docid: 56420
negative_passages.text: Is $\mathbb{Q}(\sqrt[3]{3}, \sqrt[4]{3})$ a Galois extension of $\mathbb{Q}$
negative_passages.docid: 56647
negative_passages.text: Structure of $Gal(\mathbb{Q}(\zeta_{15})/\mathbb{Q})$?
negative_passages.docid: 39719
negative_passages.text: If $g$ is a primitive root of $p^2$ where $p$ is an odd prime, why is $g$ a primitive root of $p^k$ for any $k \geq 1$?
negative_passages.docid: 622
negative_passages.text: Galois Group of $\sqrt{2+\sqrt{2}}$ over $\mathbb{Q}$
negative_passages.docid: 127198
negative_passages.text: What is $\mathbb{C}^{Aut(\mathbb{C}/\mathbb{Q})}$?
negative_passages.docid: 69067
negative_passages.text: Principal $n$th root of a complex number
negative_passages.docid: 124230
negative_passages.text: What is $\operatorname{Hom}_\mathbb{Z}(\mathbb{Q}/\mathbb{Z},\mathbb{Q}/\mathbb{Z})$?
negative_passages.docid: 100573
negative_passages.text: Show that $x^4-10x^2+1$ is irreducible over $\mathbb{Q}$