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.
How come? They are part real numbers, what would you call the other part?
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".
Iirc Gauss suggested "lateral numbers". Not the worst idea, but it's too late now.
Twisted ? Rotated ?
I mean that they're not really numbers.
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.