Question

why do we neglect the imaginary component of wave functions

Answer 1

We don't neglect it. We imagine the wavefunction as having real dimension and one complex dimension.

Rather it will will be more specific if I say that the wavefunction EVOLVES in the real dimensions and one complex dimensions.

This is why is is hard to imagine the wavefunction as a physical thing. What actually matters is not the wavefunction but the probability distribution which is given by the (psi)^2.

So to get the magnitude we find the complex conjugate of wavefunction and multiply it with the real wavefunction eliminating the complex part and giving us the magnitude.