I haven't really studied complex numbers yet, but their odd nature fascinates me. From what I understand, every complex number has an imaginary unit i, where i = , and they're written in the form a + bi.
My question is, how are the complex numbers plotted on the number line? Or do they even go on the number line? Because all the irrationals fill in the gaps for the real numbers, so there wouldn't be any room left. Maybe the number line is extended into a "number plane", where the complex numbers wouldn't be plotted as points on the line but instead on the plane; a bit like cartesian coordinates?
And one last thing; how would you compare the complex numbers with the ordinary real numbers? How can you figure out which one is greater or smaller from the other?