Indeed, nowadays no electrical engineer could get along without complex numbers, and neither could anyone working in aerodynamics or fluid dynamics.

I certainly do care about measuring educational results. But what is an 'educational result?' The twinkling eyes of my students, together with their heartfelt and beautifully expressed mathematical arguments are all the results I need.

The linear-programming was - and is - perhaps the single most important real-life problem.

There can be very little of present-day science and technology that is not dependent on complex numbers in one way or another.

Calculus works by making visible the infinitesimally small.

The whole apparatus of the calculus takes on an entirely different form when developed for the complex numbers.

What makes it possible to learn advanced math fairly quickly is that the human brain is capable of learning to follow a given set of rules without understanding them, and apply them in an intelligent and useful fashion. Given sufficient practice, the brain eventually discovers (or creates) meaning in what began as a meaningless game.