Question: fourier transform of signals

The fourier transform of a signal results in an answer with Real and Imaginary parts.

When I want to plot those results, is it correct that I need to take sqrt(Re^2 + Im^2)  ? 

However, if I just plot the Real parts of the answer why is that not correct?  Of course half the answer is missing, the imaginary part? but since it's imaginary it's not really that real and so why should it be included? 

Can someone shed some quick light on that subject for me? 

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