In both parts you need commutativity. So,

For (i), what you need to show is that if then there exists such that . Can you see why this is what you want to do? Now, you will need to use the binomial theorem for this, and basically you want to pick to be sufficiently large. Can you think of an that would work, and can you prove that it works? (As a small help, remember that if then for all (assuming )).

For (ii), you need to prove that if then for all . This actually falls out pretty easily, if you remember that your ring is commutative, and that ...