Fourier transform of a real signal

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Taking a Fourier-transform of a real signal, gives me a spectrum that has symmetry.

If I take the FFT of a real signal, then throw away half of the spectrum, and then do an inverse transform I get a complex-signal.

I go from r(t) to rc(t) where rc(t) is a complex-signal.

Now this complex-signal supposedly contains all the information to reconstruct the original real-signal. My question is, how?
 
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