Who's good with proofs?

[Sam Finch]

I'm doing some wierd maths, trying to map groups onto sets of hypercomplex numbers, (If you don't know what a hypercomplex number is don't wory you can still help)

I need some help trying to prove this statement

For any number r where (r^n = 1) any number expressible as a polynomial in r (ie - a + br + c(r^2) + ... + d(r^(n-1)) can be expressed in the form (x + yr)


where a,b,c,d and x and y are real numbers.


r is not neccecerally a real or complex number (but you may assume addittion and multiplication are both asossiative and commutitive)

I've attatched a gif with the formal statement in it, and I can explain a bit more If it's unclear, I don't actually know if it's true or not, so a counterexample will do fine.