Let 8 C be a primitive 8-th root of unity. (a) Determine the minimal polynomial of 8 over Q.

Let ζ8 ∈ C be a primitive 8-th root of unity.

(a) Determine the minimal polynomial of ζ8 over Q. - I have found that the min poly is x4 +1

need help With the following two parts, with a good explanation please (particularly showing the Q(8)/Q is galois)

(b) Show that Q(ζ8)/Q is Galois and determine its Galois group

(c) Determine all the subfields of Q(ζ8)