Question 20548
Evaluate:

{{{(-1/2 + sqrt(3/2)i)^3 = (-1/2 + sqrt(3/2)i)(-1/2+sqrt(3/2)i)(-1/2+sqrt(3/2)i)}}}  Multiply the first pair of parentheses.

{{{(-1/2+sqrt(3/2)i)(-1/2+sqrt(3/2)i) = (1/4 - sqrt(3/2)i + (3/2)i^2)}}} Recall that {{{i^2 = -1}}}
{{{(1/4 - sqrt(3/2)i - 3/2) = (-5/4-sqrt(3/2)i)}}} Now multiply this by the third parentheses.

{{{(-5/4-sqrt(3/2)i)(-1/2+sqrt(3/2)i) = 5/8 -(5/4)sqrt(3/2)i + (1/2)sqrt(3/2)i -(3/2)i^2}}} = {{{5/8 + 3/2 - (5/4)sqrt(3/2)i + (1/2)sqrt(3/2)i = 17/8 - (3/4)sqrt(3/2)i}}}