I certainly wouldn't claim that complex numbers are simple. I'm just claiming that they have a wide range of practical uses. I seem to remember a professor at my old uni claiming that there would be no flight without a solid understanding of imaginary numbers (the physics of flight involves solving cubics, which is the problem that led to Cardano discovering them). Also, electrical engineers use them all the time to avoid resorting to calculus. Quite often, the simplest way to prove something is with the complex form.
So yeah I find this all really interesting and I'm happy to discuss it and for you to disagree with me too. I guess it comes down to where you sit on the debate on whether maths is 'discovered or invented'. Personally I believe mathematicians make up new numbers, new geometries, new algebras all the time. And not necessarily for any practical benefit. That often comes later.....
