[77pt77]

> I learnt that they're required in quantum mechanics to explain any physical behaviour at all.

You can do QM without complex numbers as people are used to use them.

But it gets really awkward really fast.

[diedyesterday]

And even then it's only a disguise. The two degrees-of-freedom which a complex numbers has, are still there (and QM needs it for interference, etc.). There is not way getting around the number of degrees-of-freedom of a system or a theory. It's as "real" as it gets.