Need a solution as soon as possible please:

Assume we don't know how () and (o) fit with (w) and (d) except that they are generic superpositions |i) = au) + Bld) and lo) = yu) + old), where a, B, y and o are unknown complex numbers. You can assume |/) and () take their usual form (with real amplitudes). (a) Build an argument based on probabilities that shows a*o = (*B = y*y = 8*8 = 1/2. (b) By similar arguments, and using the result above, show that o*B + oB* =y*8 + yo* = 0. (c) Show that a*B and y*8 must each be pure imaginary. (d) Use your argument in c) to show that a and B (and likewise y and 8) cannot both be real. In other words, show that we must go into complex amplitudes for these