1. The problem statement, all variables and given/known data This is, strictly speaking, not a homework question. I have already solved this, but I think that there is a much better method to solve it. In the equation below, what relationship must w and q satisfy? If the question is not clear, please read the bottom of the post. 2. Relevant equations Exp[-i*q*t]+Exp[-i*w*t]=-2 3. The attempt at a solution I turned everything into cosines and sines, and used the trigonometric sum to product formulas. In case the question isn't clear, the answer is w/q= (2m-1)/(2n-1), where m and n are positive integers and not equal to each other.