If you want to define the number of automorphisms, the most basic thing is to know that identity maps are automorphisms, and then you only need to find non-identity maps.
Firstly, it is proved that the automorphism of Q has only one unit mapping, because f(0)=0 and f( 1)= 1. Then, for positive integers m, n,
F(mx)=f(x)+...+f(x)=mf(x), and it can be deduced that f(m)=mf( 1)=m,
Then f (1) = f (n/n) = nf (1/n) gives f( 1/n)= 1/n, so f(m/n)=m/n,
Finally, x> is at 0 and f (-x) = f (0)-f (x) =-x.
If f is an automorphism of Q(i), then according to the above discussion, f must be an automorphism on q. In this case,-1=f(- 1)=f(i)f(i), it can be obtained that f(i)=i or f(i)=-i, and f is composed of f (.
Don't say another question, you can do it yourself, even asking such a question is mindless.