1. The problem statement, all variables and given/known data Let c be a primitive 16th root of unity in the field of complex numbers. Show that c is a constructible number. 2. Relevant equations 3. The attempt at a solution I showed that c^2 is a primitive 8th root of unity and c^4 is a primitive 4th root of unity, so if I can show that one of these is constructible then I can use the fact that the square roots of constructible numbers are constructible to show that c is constructible. That being said, I am quite out of my area of knowing here, I don't have any clue how to go about showing any of these are constructible. Well, if 4 is a primitive 4th root of unity is constructible, that would mean that some kind of diamond is constructible in the complex plane? Am I on the right track here?