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Question is (a) and (b) below. From Galois Theory (2nd Ed.), Rotman

Let B = Q(iv/5). Recall (see Q.3) that B is a subfield of the splitting field E of f(z) = z* 5 Q[z]. (a) Show that |Gal(E/B)| = 2. (b) Describe the nontrivial automorphism o Gal(E/B). That is say what o is doing to the generators of F. Consider the polynomial f(x) = x4 -5 E Q[x] and let E = Q(i, v5) be its splitting field over