I'm studying for an abstract algebra exam, and I came a cross this question that I dont understand, I feel lost. I wonder if u can help me with it . I need a detailed explanation please.

thank you.

1.

a) let K be the splitting field of the polynomial x^4-2x^2-1. let F=Q(i). Show that K is a Galois extension of F. Determine Gal(k\F).

b) determine Gal(K\Q). determine the lattice of subgroups of Gal(K\Q) and give the corresponding fixed subfields of K.