1. The problem statement, all variables and given/known data Let 0 < r < 1. Show that from n=1 to n=∞ of Σ(r^ncos(n*theta)) = (rcos(theta)-r^2)/(1-2rcos(theta)+r^2) Hint. This is an example of the statement that sometimes the fastest path to a “real” fact is via complex numbers. Let z = reiθ. Then, since r = |z|, and 0 < r < 1, the series n=1 to n=∞ Σz^n converges to 1/(1−z). 2. Relevant equations z = x+iy Not really sure what else yet... 3. The attempt at a solution So here, I understand the first step is to look at the sum from n=0 to n=∞ of z^n and that we know converges to 1/(1-z) when |z|<1. My question is how do I split this up into real and imaginary forms to solve this problem. Do I split it up in the summation such that from n=0 to n=∞ Σ (x+iy)^n = the sum from n=0 to n=∞ Σx^n + the sum from n=1 to n=∞ Σ(iy)^n and then find the solution that way?