Proving Modulus of Rational Expression is Equal to 1

[Poopsilon]

Homework Statement

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

Homework Equations

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).

 

[Mark44]

Homework Statement

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

Homework Equations

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).

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

 

[Poopsilon]

This has been solved over at math stack exchange: http://math.stackexchange.com/questions/130561/prove-or-disprove-that-left-frace2i-theta-2ei-theta-1e2i-theta.