SOLUTION: simplify the expression, ( 1/2 - 3(cube root)/ 2 *i)3( to the third power.) so the question says... one half minus to the cube root of three over 2 multiplied by "i". all

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: simplify the expression, ( 1/2 - 3(cube root)/ 2 *i)3( to the third power.) so the question says... one half minus to the cube root of three over 2 multiplied by "i". all       Log On


   

Question 195121: simplify the expression,
( 1/2 - 3(cube root)/ 2 *i)3( to the third power.)

so the question says... one half minus to the cube root of three over 2 multiplied by "i". all to the third power.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Are you sure that it's not a square root and the expression is %281%2F2-%28sqrt%283%29%2F2%29%2Ai%29%5E3??? If so, then...


Take note that cos%2860%29=1%2F2 and sin%2860%29=sqrt%283%29%2F2. So this means that



%281%2F2-%28sqrt%283%29%2F2%29%2Ai%29%5E3 Start with the given expression.


%28cos%2860%29-sin%2860%29%2Ai%29%5E3 Replace 1%2F2 with cos%2860%29. Replace sqrt%283%29%2F2 with sin%2860%29 (see above)


cos%2860%2A3%29-sin%2860%2A3%29%2Ai Use De Moivre's formula to expand.


cos%28180%29-sin%28180%29%2Ai Multiply


-1-0%2Ai Evaluate the trig functions.


-1 Simplify


So %281%2F2-%28sqrt%283%29%2F2%29%2Ai%29%5E3=-1