Home › MCQs › ECAT Mathematics › Question #778
Back to Questions
ECAT Mathematics QUESTION #778
Question 1
\(\left(\dfrac{1 - \sqrt{3}i}{2}\right)^4 = ?\)
  • \(\dfrac{-1 + \sqrt{3}i}{2}\)✔️
  • \(\dfrac{-1 - \sqrt{3}i}{2}\)
  • \(\left(\dfrac{-1 + \sqrt{3}i}{2}\right)^2\)
  • None
Correct Answer Explanation
\(\dfrac{1-\sqrt{3}i}{2}\) is a complex cube root of unity \(\omega^2\), so \((\omega^2)^4 = \omega^8 = \omega^2 \cdot \omega^6 = \omega^2 = \dfrac{-1+\sqrt{3}i}{2}\).