That's a mix of complete nonsense and meaningless truism. Sure, imaginary numbers are based on the axioms for real numbers. But using other axioms ("number lin

That's a mix of complete nonsense and meaningless truism. Sure, imaginary numbers are based on the axioms for real numbers. But using other axioms ("number line" is a visualization aid appropriate for grade school, not for a serious mathematical discussion) would most definitely NOT allow us to solve exactly the same physics and engineering problems, or have the same outcomes for the same problems.