1) Find more than two automorphisms of A.
2) Do automorphisms of C fix A∩R?
The Attempt at a Solution
I managed to figure out the second question since a map which preserves the additive structure of C will fix Q. And since the maps preserves multiplicative structure as well, it is not difficult to show that the automorphism will fix A∩R. So I think I have this part covered.
So right now, I could use some help managing the first part of this problem. My professor indicated that there are a lot of automorphisms of A, so I'm thinking that there might be a family of automorphisms which aren't too difficult to construct. Any pointers on how to get started with this part are appreciated.