I'm trying to change the pitch of a signal using a Fourier Transform followed by an Inverse Fourier Transform.

I've found many examples, some of which zero out the right half of the real and imaginary bins before changing the pitch. For example, if the signal was $8192$ bins, the real and imaginary parts from $4096$ to $8192$ are set to $0$. This seems to make the math for pitch changing easier, but reduces the volume. This seems to be corrected by multiplying the magnitude by $2$.

I'm wondering what effect wiping the right half of the bins has on the final signal, apart from reducing the volume. I am confused why these bins exist if they can be wiped without affecting the final signal too much.