Question

Why we cannot tell with complex number is bigger than others?

Answer 1

Answer:

I've always had this doubt. It's perfectly reasonable to say that, for example, 9 is bigger than 2.

But does it ever make sense to compare a real number and a complex/imaginary one?

For example, could one say that 5+2i>3 because the real part of 5+2i is bigger than the real part of 3? Or is it just a senseless statement?

Can it be stated that, say, 20000i is bigger than 6 or does the fact that one is imaginary and the other is natural make it impossible to compare their 'sizes'?

It would seem that the 'sizes' of numbers of any type (real, rational, integer, natural, irrational) can be compared, but once imaginary and complex numbers come into the picture, it becomes a bit counter-intuitive for me.

So, does it ever make sense to talk about a real number being 'more than' or 'less than' a complex/imaginary one?