The complex numbers prefigured other "hypercomplex" number systems by several centuries. And the modern 2-dimensional view of them was only described close to the year 1800. Before that, they were purely algebraic.
The video (I briefly skimmed it) shows that they were invented to solve a problem in algebra. Nobody thought of them as being 2D back then.
I'm not a historian or anything, but your claim is textbook "whig history" -- and as far as I can understood you, I already proved you wrong in a previous comment.
I am not sure where this aggressive condescension is coming from. You appear to be conflating the inherent multi-dimensionality of complex numbers with their geometric/2D spatial visualization, which came later. I'm pretty sure we are in agreement here.
The video (I briefly skimmed it) shows that they were invented to solve a problem in algebra. Nobody thought of them as being 2D back then.
I'm not a historian or anything, but your claim is textbook "whig history" -- and as far as I can understood you, I already proved you wrong in a previous comment.