[angry_octet]

It's really bad that the author propagates the idea that complex numbers are not real physical phenomena because maths uses the term 'imaginary'.

[ivalm]

It's a bit different. To have real eigenvalues (ie all observables) you need to have hermetian operators. They were working on the hamiltonian operator, which is hermetian since its eigenvalues are energies (ie are observable and are thus real numbers)