Comment by phailhaus

Even simpler, complex numbers are really 2D vectors with addition and multiplication defined: a field. There's nothing "imaginary" about that second dimension, very frustrating to see them defined that way because it makes people think of it as an "escape hatch" out of real numbers. When you're working with complex numbers, you are working with a different system: `5 + 0i` is still a complex number because it's really `(5, 0)`.