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I'm having trouble understanding the Fourier transform of a function where the result in the frequency domain has imaginary components.

For example, if you take the Fourier transform of Sin[t] , the result isWhat does this mean? I can't really graph it, so I am having trouble understanding it.Code (Text):I Sqrt[\[Pi]/2] DiracDelta[-1 + \[Omega]] -

I Sqrt[\[Pi]/2] DiracDelta[1 + \[Omega]]

I can grasp a regular Fourier transform; it simply tells you what components are making up your signal wave. But when an imaginary I is thrown in there, what happens? How can the superposition of all those waves give you the real signal wave?

Does anybody have an intuition they could share?

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# Intuition for imaginary part of Fourier Transformation?

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