1. Let Va = (2+ 31) m / and Vs = (4-5i) m 1/2 (a) Find 4* and Yoda- (b) Find |4 4,) and compare with |4ally.)- (c) Find (Vava)* and compare with Vod. (d) Express V. in the form V. = Re -. Find the real number R. and at least two possible values for the real number Va. Explain why d. is not uniquely defined. [5 points) 2. The effective mass of a quasi-electron confined in a 20 mm long semiconductor nanowire is m" 0.065 mo, where my is the free electron mass. (a) Compute the energy of the ground, first excited, and second excited states. Give the results in meV. (b) Compute the energies and wavelengths of the light emitted when a quasi-electron experiences the following transitions: (i) from the first excited state to the ground state and (ii) from the second excited state to the ground state. Note: The free electron mass is my = 9.1 x 10 kg [ 5 points]