# Complex Numbers, Hermitian matrix

Hi guys, Can you please help with the following problem:

Given: βπ (π) π^(βπ(2πβ_π π+π_0))+π_π (π)

Required Result: |π¦(π)|^2=|β|^2 |π (π)|^2+|π_π (π)|^2+2β[βπ (π) π^(βπ(2πβ_π π+π_0))+π_π^π» (π)]

My Solution: I used the following rule of complex numbers: |π§_1+π§_2 |^2=|π§_1 |^2+|π§_2 |^2+2π (π§_1 (π§_2 )Β Μ ) I assumed that π§_1=βπ (π) π^(βπ(2πβ_π π+π_0)), and π§_2=π_π (π). So, |π§_1 |^2 γ=|βπ (π) π^(βπ(2πβ_π π+π_0)) |γ^2=|β|^2 |π (π)|^2 π^(β2π(2πβ_π π+π_0)) |π§_2 |^2=|π_π (π)|^2 π§_1 (π§_2 )Β Μ =|β|^2 |π (π)|^2 γ|π_π (π)|^2 πγ^(β2π(2πβ_π π+π_0)) |π§_1+π§_2 |^2=|π§_1 |^2+|π§_2 |^2+2β(π§_1 (π§_2 )Β Μ )=|β|^2 |π (π)|^2 π^(β2π(2πβ_π π+π_0))+|π_π (π)|^2+2β(|β|^2 |π (π)|^2 γ|π_π (π)|^2 πγ^(β2π(2πβ_π π+π_0)) ) but I couldnβt reach the same result in Green. (1) How was the first term of the real part ββπ (π) π^(βπ(2πβ_π π+π_0))β obtained? (2) How was the second term of the real part βHermitian matrix π_π^π» (π")β obtained"? I appreciate your help.

Please define objects one by one, using LaTeX is a good idea. Also, please try to isolate one sage-related question, best also showing sage code and the point where the coding became an issue. There is no result in Green. Which is the origin of the question, and why should it be related to sage?