Let f be in R[x] and suppose a+bi is a complex root of f with a,b in R and b not equal to 0. Prove that a-bi is also a root of f.

I let h = (x-(a+bi))(x-(a-bi)). I know I need to show h is in R[x] in order to apply the division algorithm to f and h in R[x], but I'm stumped on how to do that.