Marvel at the magic for a moment. The singlet state looks the same no matter what basis you pick. Next, let us practice taking inner products with kets of multiple spins. Use (n) = cos;| +z > +sing| -z> and |0,0 >= 4 (|+2, -z > -|- z, +z >). Compute the following I - ny = Sin 8 1+27 - cos 2 1- 27 . (+n, -= 10, 0) . (+n, +210, 0) . (-n, -2/0,0)