Poopsilon said:Homework Statement
Prove [tex]|\frac{e^{2i\theta} -2e^{i\theta} - 1}{e^{2i\theta} + 2e^{i\theta} -1}| = 1[/tex]
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).
The modulus of a rational expression is the absolute value of the expression, which means that any negative values in the expression are turned into positive values. It represents the distance of the expression from zero on a number line.
Proving that the modulus of a rational expression is equal to 1 is important because it helps to simplify and solve equations involving rational expressions. It also allows us to determine the behavior of the expression and its graph.
To prove that the modulus of a rational expression is equal to 1, we need to show that the numerator and denominator of the expression are equal in absolute value. This can be done by simplifying the expression and checking if the resulting numerator and denominator are equal.
Some common techniques used to prove the modulus of a rational expression is equal to 1 include simplifying the expression, factoring the numerator and denominator, using the properties of absolute value, and using the definition of modulus.
Yes, the modulus of a rational expression can be something other than 1. It can be any positive value, depending on the expression. However, in order to prove that the modulus is equal to 1, we need to show that the numerator and denominator are equal in absolute value.