That's true, but irrelevant. Complex numbers aren't "necessary for the continuum" as you put it, and some realists might argue that they don't hold the same "d

That's true, but irrelevant. Complex numbers aren't "necessary for the continuum" as you put it, and some realists might argue that they don't hold the same "discoverability" as the reals. I wouldn't. I think the reals and the complex numbers have the same "realness" and that neither represents any innate property of the physical world, despite how obviously useful they are in physical models.