I ran into some trouble understanding how my professor went from this step in his...

Darian Hubbard

Darian Hubbard

Answered

2022-07-21

I ran into some trouble understanding how my professor went from this step in his solution:
π π | 1 2 π e i m x 1 2 π e i n x | 2 d x
π π | 1 2 π e i m x 1 2 π e i n x | 2 d x
to this step:
π π 1 2 π ( 1 e i ( m n ) x e i ( n m ) x + 1 ) d x
I cannot see how this was done, please help!

Answer & Explanation

kamphundg4

kamphundg4

Expert

2022-07-22Added 20 answers

I would recommend using the complex conjugate to calculate the squared absolute value.
π π | 1 2 π e i m x 1 2 π e i n x | 2 d x
π π ( 1 2 π e i m x 1 2 π e i n x ) ( 1 2 π e i m x 1 2 π e i n x ) d x
π π ( 1 2 π 1 2 π e i ( n m ) x 1 2 π e i ( m n ) x + 1 2 π ) d x
π π 1 2 π ( 1 e i ( m n ) x e i ( n m ) x + 1 ) d x

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