Describe the element in $Q (a^{ 1/ n}, w)$ where $w=\exp ((2\pi i )/n )$
The basis of
$Q (a^{ 1/ n}, w) $= ${(1, a^{ 1/ n}, ...,(a^{ 1/ n})^{n-1}, w,w^2,.....w^{n-1}, a^{ 1/n} w ,a^{1/ }w^2 ,....,{a^{ 1/ n}}^{n-1} w^{n-1}, .... . {a^{ 1/ n}}^{n-1}w^{n-1}})$
Is it true ? If not, what is the correct solution? Thanks in advance.