Fourier Series Complex Exponential Form Question

[jungykang]

Quick question about the complex exponential form of the fourier series. After finding coefficient Cn, and plugging back to the function f(x)=sigma(n=-infinity to inifinty)Cn*e^iwnx, are the imaginary terms simply discarded?

 

[HallsofIvy]

If you are assuming that your original function is a real-valued, then the imaginary terms should sum to 0.

 

[jungykang]

Thanks so much for the help!

 

[Ishuda]

Not that it really adds anything but just because I feel like rambling a bit - In a practical sense; yes, just throw the imaginary terms away assuming your original function is real-valued. Of course the justification for this is as HallsofIvy pointed out but why spend time computing zero.