We know the solutions of geometrically form a regular decagon. It it possible to generate the solutions of (for example) by applying some type of symmetric group action on the decagon?
Oh, well, I'd just interpret it as and apply the first geometric interpretation, perhaps using a change of variable to make it look like .
Anyway, geometrically what would happen is that instead of your solutions lying on the circle of radius 1 in the complex plane, they will lie on the circle of radius