[andreareina]

I've heard physicists talk about what's real as the set of concepts/objects that are required to describe and predict the world. So imaginary numbers are real (if you believe the qm wave function is real), infinities aren't (but are still very useful).

[LeegleechN]

There are always alternative ways to describe the same phenomena. For example QM could be done with only real numbers (you can emulate imaginary numbers with matrix operations). There is no clear cut notion of what is "required".