Do imaginary numbers have more significance in the universe than just a simple mathematical convenience?

The square root of minus one, and hyperbolic functions in general ,seem to be at the (mathematical) heart of virtually all modern physics .

Is it simply a "thought up", mathematical convenience , or does it actually point to something "real" and fundamental about the universe? .
Update: Edit : What I'm getting at here is that without imaginary numbers and hyperbolic functions -- virtually all modern theories in physics and cosmology would be impossible . That is , we had to have invented this branch of mathematics, just to make the universe understandable to us. Is it therefore just a... show more Edit : What I'm getting at here is that without imaginary numbers and hyperbolic functions -- virtually all modern theories in physics and cosmology would be impossible . That is , we had to have invented this branch of mathematics, just to make the universe understandable to us.

Is it therefore just a coincidence that this form of mathematics "works" when looking at what makes the universe tick, or is it because its language is particularly "in tune" with it for some reason?
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