But there is definitely something lacking from reducing everything down to a one dimensional measure. For instance, there are many pieces of real estate improvements that ought to be torn down and replaced with new improvements (homes, commercial buildings, etc). But the economy rarely offers incentives or even the abilities to tear down and rebuild - despite the huge benefit construction is to an economy. For things like this, I conclude the economic system is not closed. It’s not creating a self sustaining relationship between all participants.
A lot of the confusion in this thread seems to come from people believing that the main idea of complex numbers is that they are just pairs of real numbers.
That is wrong -- pairs of real numbers are just pairs of real numbers. Complex numbers are pairs of real numbers with a particular multiplicative structure.
I should have added that it only becomes circular if you add the point at infinity. Otherwise it’s more similar to a plane. But yes, it’s not simply x,y numbers when you assume y^2=-1. The geometric interpretation of the complex numbers matters, and you have to do it correctly. Gets very hard to imagine quickly.
If you start at 1+0i and multiply twice by 0+1i, you end up at -1+0i. If you try to imagine this in the xy plane (where we pretend x and y are currencies) then this would mean that multiplying a positive amount of one currency (1x + 0y) by a positive amount of another currency (0x + 1y^2) would put you in debt (-1x + 0y). This would be a very strange property to have in your currency!