Complex/imaginary numbers are just badly named for historical reasons, they represent an objectively central concept in math and physics, and can be derived from axioms of what we expect from a well-behaved number field. For reals, we have: (A) expected properties of addition and multiplication, (B) total order and other order-related nice properties (Dedekind-complete). Any mathematical structure satisfying (A,B) will be equivalent to real numbers. Now if we extend it to get (C) algebraic closure, so that all polynomials have roots, we get the complex numbers.