I find this "spiral" concept showing up in other cases as well, and I agree that it's under-rated (or under-studied) as a way to understand the complex numbers. By thinking about periodic points on a complex spiral, you can extend many useful properties of polynomials to those with rational coefficients. We can begin to talk about the roots of equations like x^(3/2) + x^(1/2) = 0 and we find results that very naturally extend from roots of similar "standard" polynomials. We can see that x^(1/2) = 0 has half as many roots as x^1 = 0, and x^(1/4) = 0 has half again as many roots, even if they all "project" down to 1 -- their periodicity on the spiral is 4pi and 8pi instead of the standard 2pi. I feel like there's a lot going on there that hasn't been explored.