I don't know what exactly your prof has in mind when he says this: it's a complex subject, so I imagine it's difficult to explain!
I think what he may have meant by "play" is that we can do maths on the "Imaginary" numbers (just as we can with "Real" numbers), but when we measure things we are getting "Real" numbers and when we want to interpret our calculations in terms of actual measurements, we have to convert our results into "Real" numbers.
I think it is unfortunate that the word "Imaginary" is still used to describe these numbers. That was a half apologetic, half derisory description (depending on whether you liked them or not) given to them when they were first thought about. But after a 400 years they are not just accepted, but are a foundation for large areas of maths. Other numbers have also had very sceptical reception when they first came into use. It's fairly obvious (to people 100's of years ago) that you can't have 0: if you haven't got any then you haven't got anything, you can't say I've got 0 when you haven't got anything. And when people started talking about negative numbers... how can I have -2 cows? It's just crazy!
Equally "Real" is just a mathematical label for a type of number that you need (beyond integers) when you measure things in the real world. Most of maths (all of it?) is really an abstraction of the real world thought up in the imagination of people. So "Imaginary" numbers are no more imaginary than "Reals" or any other bit of maths.
I don't know whether to say "don't worry" or "hang on to your hat!", because you are going to come across more wierd stuff before long. You've probably already had negative time and maybe you didn't worry about that, but what about negative frequencies? A radio wave that's un-oscillating a million times a second? But once you let the mathematicians have their fun and "play" with these things, they find all sorts of useful results and make calculations a lot easier.
