SOLUTION: I have no clue how to do this and my homework is due in a day and a half please show me how to do this type of problem (-1/2+sqrt(3/2)i)^3= _____+_____

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Question 20548: I have no clue how to do this and my homework is due in a day and a half please show me how to do this type of problem (-1/2+sqrt(3/2)i)^3= _____+_____
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
Evaluate:
%28-1%2F2+%2B+sqrt%283%2F2%29i%29%5E3+=+%28-1%2F2+%2B+sqrt%283%2F2%29i%29%28-1%2F2%2Bsqrt%283%2F2%29i%29%28-1%2F2%2Bsqrt%283%2F2%29i%29 Multiply the first pair of parentheses.
%28-1%2F2%2Bsqrt%283%2F2%29i%29%28-1%2F2%2Bsqrt%283%2F2%29i%29+=+%281%2F4+-+sqrt%283%2F2%29i+%2B+%283%2F2%29i%5E2%29 Recall that i%5E2+=+-1
%281%2F4+-+sqrt%283%2F2%29i+-+3%2F2%29+=+%28-5%2F4-sqrt%283%2F2%29i%29 Now multiply this by the third parentheses.
%28-5%2F4-sqrt%283%2F2%29i%29%28-1%2F2%2Bsqrt%283%2F2%29i%29+=+5%2F8+-%285%2F4%29sqrt%283%2F2%29i+%2B+%281%2F2%29sqrt%283%2F2%29i+-%283%2F2%29i%5E2 = 5%2F8+%2B+3%2F2+-+%285%2F4%29sqrt%283%2F2%29i+%2B+%281%2F2%29sqrt%283%2F2%29i+=+17%2F8+-+%283%2F4%29sqrt%283%2F2%29i