We could've called the imaginaries "orthogonals", "perpendiculars", "complications", "atypicals", there's a million other options. I like the idea that a number is complex because it has a "complicated component".
Usually they explain it something like: oh, at first people didn't know what 2-5 added up to, but then we invented negative numbers. Well, complex numbers are that but for square roots of negative numbers.
But that's a completely misleading way to explain these things. Complex numbers aren't numbers aren't numbers really.
It entirely depends on what we mean for something to be a number. Humans over the passage of time have been recognizing that their earlier conception had been too restrictive, narrow minded.
As one broadens the idea of what it means for anything to be a number, we acquire/invite new members to the family and with great benefit.
I mean, yeah, they aren't real numbers, they are composed of a real number and another one that is the multiplicative of the square root of -1. Hence they're called complex, i.e. composed of parts.
If the square root of -1 is not a number, what is it? How come you can do arithmetic with it?
