1. The problem statement, all variables and given/known data Show that linear combinations A-iB and A+iB are not hermitian if A and B (B≠0) are Hermitian operators 2. Relevant equations Hermitian if: A*=A Hermitian if: < A l C l B > = < B l C l A > 3. The attempt at a solution So I've seen this question everywhere but not the solution to it. I get that the solution isn't (A+iB)* = (A*+i*B*) = (A*-iB*) (since i*=-i) So that's not helping me prove all its non-hermitianess, but it doesn't seem right since if I changed the order of the Hermitian: < +iB l C l A > ≠ < A l C* l -iB > Is that where I should be going with this? Or am I completely going wrong? I know it's against the rules, but could someone show me the solution? I've been stuck on this for an entire day now and I'm fed up. Thanks a lot!