An anti-hermitian (and skew-hermitian) operator is equal to minus its hermitian conjugate: (a) Show that the expectation value of an anti-hermitian operator is imaginary. (b) Show that the eigenvalues of an anti-hermitian operator are imaginary. (c) Show that the eigenvectors of an anti-hermitian operator belonging to distinct eigenvalues are orthogonal. (d) Show that the commutator of two hermitian operators is anti-hermitian. How about the commutator of two anti-hermitian operators