The splendor of true

A nice contributor pointed out that the imaginary universe based on i, which is an interesting idea to find roots to equations that do not have any, that is to say, roughly, to find the roots of the symmetric curve pointed at $(0,y) in the Hachel system.
Although physicists use incorrect complex products, since for me, the real part of a complex product is (aa'+bb'), and not (aa'-bb'), they nevertheless manage to find pretty figures.
So I wondered, what would happen if, instead of working with their equations, we worked with mine.
Into what strange world would we fall, if, instead of using Z=aa'-bb'+i(ab'+a'b), we used the much more logical and natural equation Z=aa'+bb'+i(ab'+a'b).
How would the "Mandelbrot" or the "Julia" obtained be less pretty?
Isn't beauty the splendor of truth?
R.H. (suivi sci.math)