SOLUTION: Can u help me with this question Express {{{1/(1-i*sqrt3)^3}}} in the form a/b where, a,b is the subset of positive real number, Z.

Algebra ->  Square-cubic-other-roots -> SOLUTION: Can u help me with this question Express {{{1/(1-i*sqrt3)^3}}} in the form a/b where, a,b is the subset of positive real number, Z.      Log On


   

Question 388808: Can u help me with this question
Express 1%2F%281-i%2Asqrt3%29%5E3 in the form a/b where, a,b is the subset of positive real number, Z.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F%281-i%2Asqrt%283%29%29%5E3
=1%2F%282%281%2F2+-+i%2Asqrt%283%29%2F2%29%29%5E3
=1%2F%288%2A%28cos%28-60%29+%2B+i%2Asin%28-60%29%29%5E3%29
=1%2F%288%2A%28cos%28-60%29+%2B+i%2Asin%28-60%29%29%5E3%29
=1%2F%288%2A%28cos%28-180%29+%2B+i%2Asin%28-180%29%29%29 by de Moivre's Theorem
=1%2F%288%2A%28-1%2B0%29%29
=-1%2F8.