How do you visualize negative Frequency in Time domain ?

In the field of Digital signal processing I have seen people using words

Complex signals and Negative frequencies. For eg. in FFT Spectrum.

Does it really have significant meaning in the time domain or is just a part of the mathematical symmetry.

How do you visualize negative Frequency in Time domain ?

Answer

FFTs work by treating signals as 2-dimensional -- with real and imaginary parts. Remember the unit circle? Positive frequencies are when the phasor spins counter-clockwise, and negative frequencies are when the phasor spins clockwise.

If you throw away the imaginary part of the signal, the distinction between positive and negative frequencies will be lost.

For example (source):

If you were to plot the imaginary part of the signal, you would get another sinusoid, phase shifted with regards to the real part. Notice how if the phasor were spinning the other way, the top signal would be exactly the same but the phase relationship of the imaginary part to the real part would be different. By throwing away the imaginary part of the signal you have no way of knowing if a frequency is positive or negative.