Question

If $\alpha$ is a nonreal cube root of unity then$|{\alpha }^n|,nϵZ$ is equal to

• A. $1$
• B. $3$
• C. $0$
• D. None of these

Answer 1

The correct option is A $1$

Non real cube root of unit is $\omega$.
${\omega }^n$ is either $\frac{1+\sqrt{3}i}{2}$ or $\frac{1-\sqrt{3}i}{2}.$
$(\cos \frac{\pi }{3}\pm i\sin \frac{\pi }{3}{)}^n=\cos \frac{n\pi }{3}\pm i\sin \frac{n\pi }{3}$
$|\cos \frac{n\pi }{3}\pm i\sin \frac{n\pi }{3}|=1$