Incorrect. You can construct an isomorphism between the even subalgebra of the 2D geometric algebra Cl(2) and the complex numbers that maps 1 to the unit scalar and i to the pseudoscalar: https://link.springer.com/article/10.1007/BF01883676

nope, they’re just one mathematical construct out of many (e.g. 2D vector calculus or geometric algebra), and they just happened to stick

actual theoretical physicist here: “imaginary numbers” are just poorly named, there’s nothing imaginary about them. You might as well use 2D geometric algebra to do the exact same job (treating real numbers as scalars and imaginary numbers as pseudoscalars)