SOLUTION: {{{ (1/2 + (sqrt(3)/2) i )^2 }}}

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson  -> Lesson -> SOLUTION: {{{ (1/2 + (sqrt(3)/2) i )^2 }}}      Log On


   

Question 256096: +%281%2F2+%2B+%28sqrt%283%29%2F2%29++i+%29%5E2+
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

+%281%2F2+%2B+%28sqrt%283%29%2F2%29++i+%29%5E2+

+%281%2F2+%2B+%28sqrt%283%29%2F2%29++i+%29%281%2F2+%2B+%28sqrt%283%29%2F2%29++i+%29

Use "FOIL":



1%2F4+%2B+%28sqrt%283%29%2F4%29i+%2B+%28sqrt%283%29%2F4%29i+%2B+%283%2F4%29i%5E2

Combine the middle terms and replace i%5E2 by -1

1%2F4+%2B+%282sqrt%283%29%2F4%29i+%2B+%283%2F4%29%28-1%29

Simplify

1%2F4+%2B+%28sqrt%283%29%2F2%29i+-3%2F4

-2%2F4+%2B+%28sqrt%283%29%2F2%29i


-1%2F2+%2B+%28sqrt%283%29%2F2%29i

Edwin