In the text we introduced electron spin states with spin ±1/2 in the ẑ-direction, |±〉, and states with spin ±1/2 in the x̂-direction, |±_x〉 = (|+〉 ± |−〉)/√2. Measuring the z-component of spin in the state |±_x〉 gives ±1/2 , each with 50% probability. The analogous states with spin ±1/2 in the ŷ-direction are |±_y〉 = (|+〉 ± i |−〉)/√2. Show that a measurement of the spin in the x̂- or ẑ direction on these two states also yields ±1/2 each with 50% probability.