Question

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

• A. 0
• B. 1
• C. 2
• D. -1

Answer 1

Answer: (D)

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