Is this ring an integral domain?

Question

I'm starting to study Algebraic number theory and I'm having problems with the first examples of this book. I'm trying to prove this is a quadratic domain, i.e., an integral domain:

I'm sorry I know this is a stupid question, but I'm a really beginner on this subject trying to study it on his own.

Thanks in advance

Answer 1

Every subring of the field of complex numbers is a domain.