1. Tardigrade
  2. Question
  3. Mathematics
  4. ((-1 +i√3/2))50 + ((-1 - i√3/2))50 =

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. $\left(\frac{-1 +i\sqrt{3}}{2}\right)^{50} + \left(\frac{-1 - i\sqrt{3}}{2}\right)^{50} = $

COMEDKCOMEDK 2010Complex Numbers and Quadratic Equations

Solution:

$\left(\frac{-1 +i\sqrt{3}}{2}\right)^{50} + \left(\frac{-1 - i\sqrt{3}}{2}\right)^{50} $
$= \left(\omega^{2}\right) ^{50} +\left(\omega \right)^{50} = \omega ^{100} +\omega ^{50}$
$ = \left(\omega ^{3}\right)^{33} \omega + \left(\omega ^{3}\right)^{16} \omega ^{2} = \omega +\omega ^{2} = - 1$