(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Addition of exponentials, and relationship between variables.

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