# Thread: Proving a symmetric property of the fourier transform

1. ## Proving a symmetric property of the fourier transform

Hello!

I'm trying to prove a symmetric property of the fourier transform, but I'm having some problems with that.
Here is the failed try of the proof: fourier - MathB.in.

Any help would be much appreciated! (:

2. ## Re: Proving a symmetric property of the fourier transform

Hey sapsapz.

I think what you have to do is show that if the final transform has no complex part that the two are equal. If you have a complex variable z = x + iy, then y = 0 implies equality for your problem.

Recall that -e^(-iwx) = -[cos(-wx) + isin(-wx)] = -cos(-wx) + 0 (if no imaginary component) = -cos(wx) since cos(x) = cos(-x).

3. ## Re: Proving a symmetric property of the fourier transform

Originally Posted by chiro
Hey sapsapz.

I think what you have to do is show that if the final transform has no complex part that the two are equal. If you have a complex variable z = x + iy, then y = 0 implies equality for your problem.

Recall that -e^(-iwx) = -[cos(-wx) + isin(-wx)] = -cos(-wx) + 0 (if no imaginary component) = -cos(wx) since cos(x) = cos(-x).
Thanks chiro, but I can't claim the final transform has no imaginary part, thats what Im trying to prove in the first place, right?
Did you see any error in the equalities chain in the proof?

4. ## Re: Proving a symmetric property of the fourier transform

Ok, solved, thanks!