Quantum Mechanics algebra - complex analysis

sxc656
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Hi,

I cannot work out how the working shown in the attached pic is well, er worked out!:confused:
Could someone explain the ins and outs of the complex analysis of taking the real or imaginary parts of some formula, for example in the context of the my case.
 

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Remember that e^{ix}= cos(x) + isin(x). Taking the imaginary part means you're looking at just the sine part. When you combine into that integral form, the solution is simpler.
 
Pengwuino said:
Remember that e^{ix}= cos(x) + isin(x). Taking the imaginary part means you're looking at just the sine part. When you combine into that integral form, the solution is simpler.

Is this what you mean, i am not sure about the last two lines of working.
 

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You can write

sin pr = Im(e^{ipr})

Because Im(z+w) = Im(z)+Im(w) and Im(az) = aIm(z) for real a, you can pull the other exponential in as well as reverse the order of I am and the integral.
 
Thanks to all:approve:
 

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