Q. One root of $(1)^{1/3}$ is
A) $\frac{\sqrt{3}i}{2}$
B) $\frac{1 + \sqrt{3}i}{2}$
C) $\frac{1 - \sqrt{3}i}{4}$
D) $\frac{- 1 - \sqrt{3}i}{2}$
Explanation
(d)
Let $z = (1)^{1/3}$
$z^{3} - 1 = 0$
$\Rightarrow \ \ \ (z - 1)\left( z^{2} + z + 1 \right) = 0$
$\Rightarrow \ \ \ z = 1,\ \frac{- 1 \pm \sqrt{1 - 4}}{2}$
$\Rightarrow \ \ \ z = 1,\ \frac{- 1 \pm \sqrt{3}i}{2}$
Hence, $\frac{- 1 - \sqrt{3}i}{2}$ is one of the root of $(1)^{1/3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.