> Why do we have to use complex numbers when the system is very much real
If you don't use complex numbers you end up with a bunch of maths that looks suspiciously like complex numbers. The algebraic properties of complex numbers make it a very natural way to express quantum mechanics.
I believe 3Blue1Brown has some good videos on the topic - you really need to learn about complex numbers separately to really see the magic of them (It's largely visual, so it's hard to transmit via text)
Edit: The book "Visual Complex Analysis" is very good if you resonate with its approach - I personally simply cannot click with almost any geometry, so it wasn't really for me although I appreciate that it's really very nice.
If you don't use complex numbers you end up with a bunch of maths that looks suspiciously like complex numbers. The algebraic properties of complex numbers make it a very natural way to express quantum mechanics.
I believe 3Blue1Brown has some good videos on the topic - you really need to learn about complex numbers separately to really see the magic of them (It's largely visual, so it's hard to transmit via text)
Edit: The book "Visual Complex Analysis" is very good if you resonate with its approach - I personally simply cannot click with almost any geometry, so it wasn't really for me although I appreciate that it's really very nice.