Did anyone else think this was going to be about algebraic roots?
The complex numbers are famously the algebraic closure of the reals, but I find myself wondering lately if there is a related thought which doesn’t privilege them over the hyperbolic numbers or the dual numbers.
You are being downvoted, but this is not as off-topic as it may seem.
Simone Weil had a brother, André Weil. You may not know his name on the top of your head, but I guarantee you that you've heard of the pseuodonym he created together with some other mathematicians: Nicolas Bourbaki.
I'm sure Weil and/or Bourbaki has lots to say about these topics.
The complex numbers are famously the algebraic closure of the reals, but I find myself wondering lately if there is a related thought which doesn’t privilege them over the hyperbolic numbers or the dual numbers.