Let $p$ be an odd prime and let $ zeta_p = e^{2 pi i/p}$ be a $p$-th root of unity. Consider the field $K = mathbb{Q}( zeta_p + zeta_p^{-1})$. a) Find a $ mathbb{Q}$-basis for the field $K$. b) Is $ zeta_p in K$? Find the degree of $ zeta_p$ over $K$.

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Let $p$ be an odd prime and let $ zeta_p = e^{2 pi i/p}$ be a $p$-th root of unity. Consider the field  $K =  mathbb{Q}( zeta_p +  zeta_p^{-1})$.  a) Find a $ mathbb{Q}$-basis for the field $K$.  b) Is $ zeta_p  in K$? Find the degree of $ zeta_p$ over $K$.

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This an additional answer to - Let $p$ be an odd prime and let $ zeta_p = e^{2 pi i/p}$ be a $p$-th root of unity. Consider the fie

(Solved): Let $p$ be an odd prime and let $\zeta_p = e^{2\pi i/p}$ be a $p$-th root of unity. Consider the fie ...

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