# Proving Modulus of Rational Expression is Equal to 1

1. Apr 11, 2012

### Poopsilon

1. The problem statement, all variables and given/known data

Prove $$|\frac{e^{2i\theta} -2e^{i\theta} - 1}{e^{2i\theta} + 2e^{i\theta} -1}| = 1$$

2. Relevant equations

3. The attempt at a solution

I feel like this should be fairly simple, anyone have any hints? Also this is just one step in an attempt to solve a much larger problem, so don't feel the need to be overly cryptic. Also that means I'm not entirely sure that it's true (but I think it is).

Last edited: Apr 11, 2012
2. Apr 11, 2012

### Staff: Mentor

I would use the facts that ei 2θ = cos(2θ) + i sin(2θ) and ei θ = cos(θ) + i sin(θ) and see where that took me.

3. Apr 11, 2012