Ok, I think I've proved that I is an ideal of R as follows:
You need to show that p+q e I, 0 e I, -p e I and rp e I where r e R and p e I
The first three are easy enough, the fourth I did the following(I think its right!)
Let r=m+2ni e R
Then rp= (m+2ni)(2a+2bi)=2ma+2mbi+4nai-4nb
=2(ma-2nb)+2(mb+2na)i which is clearly an element of I
I still don't know how to show that I is not a principle Ideal, probably because I don't know how to get the Principal Ideal!
Anyone any ideas?