In quantum mechanics, wavefunctions are complex equations that return a complex number. The wavefunctions do not hold any real meaning, but combining them with a Hermitian operator can give you a real quantity. The real or imaginary part of the equation don't signify anything and are interchangeable. It's just that complex numbers allow you to hold two dimensional values, and any other mathematical structure that allows this can be used equally well.

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It is misleading to consider the real and imaginary parts of the wave function separately. The wave function is a function of spacetime that returns a complex number. We interpret this as meaning that the wavefunction requires two components to describe it. You can think of this as an amplitude and a phase. However the split between the real and imaginary parts is arbitrary and can be changed by a coordinate transformation, so there is nothing special about the real part or the imaginary part.

The wavefunction is not an observable, so the fact it is a complex quantity does not matter. Anything we can observe is given by acting on the wavefunction with a Hermitian operator, and these are guaranteed to return a real result.

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