[UPSC CSE 2008] Angular momentum, spin etc (Q327, 20M)

$ and [\hat{L}_-, \hat{L}_z]. Show that \hat{L}_+ |l, m\rangle = \sqrt{l(l+1) - m(m+1)} |l, m+1\rangle, where |l, m\rangle is the state with definite values for L^2 and L_z.