This is in the context of QM, and that should be included in the title. "Why are amplitudes complex numbers" is meaningless, unless it's clear from the context

This is in the context of QM, and that should be included in the title. "Why are amplitudes complex numbers" is meaningless, unless it's clear from the context that we're talking about QM amplitudes. I would suggest "Why are amplitudes [in quantum mechanics] complex numbers?"