The fields Q(2) and Q(3+2) are the same, of course. Let = 3 + 2. a.

The fields Q(√2) and Q(3+√2) are the same, of course. Let α = 3 + √2.

a. Find a conjugate β ≠ α of α over Q.

b. Referring to part (a), compare the conjugation automorphism ψ_√2,-√2 of Q(√2) with the conjugation automorphism ψ_α.β.