FlufferNuterFSU
Oct24-09, 03:24 PM
1. The problem statement, all variables and given/known data
I need to simplify the expression below. The absolute value is throwing me off
\left[\left|(\alpha + k)^{2}e^{-2i \alpha a} - (\alpha - k)^{2}e^{2i \alpha a}\right|\right]^{2}
2. Relevant equations
I know \left|e^{ix}\right| = 1
3. The attempt at a solution
I know this eventually simplifies to:
(\alpha + k)^{4} + (\alpha - k)^{4} - (\alpha^{2} - k^{2})^{2}(e^{4i \alpha a} + e^{-4i \alpha a})
I need to simplify the expression below. The absolute value is throwing me off
\left[\left|(\alpha + k)^{2}e^{-2i \alpha a} - (\alpha - k)^{2}e^{2i \alpha a}\right|\right]^{2}
2. Relevant equations
I know \left|e^{ix}\right| = 1
3. The attempt at a solution
I know this eventually simplifies to:
(\alpha + k)^{4} + (\alpha - k)^{4} - (\alpha^{2} - k^{2})^{2}(e^{4i \alpha a} + e^{-4i \alpha a})