Ciro Santilli
OurBigBook.comWhy is there a complex number in the equation? Intuitively and mathematically:
Necessity of complex numbers in the Schrödinger equation by Barton Zwiebach (2017)
. Source. This useless video doesn't really explain anything, he just says "it's needed because the equation has an in it".
The real explanation is: they are not needed, they just allow us to write the equation in a shorter form, which is always a win: physics.stackexchange.com/questions/32422/qm-without-complex-numbers/557600#557600