QM is a solid theory that reliably predicts every known experiment dependent on it.

And it seems you need to brush up on your arithmetic theory. There is a progression in the usual number fields, Naturals (w/ or w/o 0), Integers, Rationals, Reals, Complex, Quarternions, Octonions, Sedenions, etc.

• Naturals have a starting point, countability, no negatives, no inverse elements and no algebraic closure.
• Integers sacrifice a starting points to gain negative elements.
• Rationals sacrifice finiteness of subsets to gain inverse elements.
• Reals sacrifice uniqueness of representation to gain uncountability.
• Complex numbers sacrifice absolute order to gain algebraic closure.

Then it gets a bit hazy in memory, but I know Quarternions sacrifice commutativity of multiplication and Octonions aren't associative but I can't remember what neat tricks you gain there. The Sedenions have zero divisors but I can't remember what they loose.

Now the point is that complex numbers are the most interesting because they have algebraic closure; you cannot construct an equation with multiplication and addition or almost any other operation in which the solution isn't a Complex number. Not so with the Reals (sqrt -1). Thus Complex numbers are completely logical to be physics rather than Reals.