Obvious error in the proof is the part "which means that .5 + sqrt(3/4)*i = -1".. Generally when x^3=y^3, you can never directly say x is always equal to y.. It only leads to the conclusion that (x^3-y^3)=0, which on factorisation leads to (x-y)*(x^2+xy+y^2)=0.. So any further solution after that particular statement is not accepted in algebra..
1st of all, we must understand that we need to ask him questions that could contain only yes or no as answers, not questions like 'What number are you thinking of?' See if this solution is logically correct..
Write down the numbers 9, 99 and 999 in 3 different pieces of paper.. Beneath the no 9, write down the question "Is 1<2?" Beneath the no 99, write down "Is 1>2?" Beneath 999, write down any question for which the person cannot answer a yes or a no with confidence, such as "Will South Africa win the next cricket World Cup?"
Now showing these 3 pieces of paper, ask the person, "Is the answer to the question beneath the number in your mind 'yes'?"
Interpretation of his answers: Yes-9; No-99; Dont know/Cant say-999..