1. The problem statement, all variables and given/known data Consider the field extension Q(c):Q, where c is a primitive nth root of unity. Is this extension normal? 2. Relevant equations 3. The attempt at a solution I believe this polynomial splits in x^n - 1,where it's n roots are exactly the powers of c. Thus this extension is normal because Q(c) is a finite splitting field of the polynomial x^n-1 over Q. Is this correct?