Question

If $\alpha$ be non real cube root of unity, then $\left|\sqrt{\alpha }\right|$ equals

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

Answer 1

Answer: (B)

$1$

Non real Cube root of unity are $w$ and $w^2$. Let us take that root be $w$ , it would also be true for $w^2$.

$w$ = -1/2 + i$\sqrt{3}/2$ = $\cos 2\pi /3$ + i$\sin 2\pi /3$

$\sqrt{w}$ = $\cos \pi /3$ + i$\sin \pi /3$ (Since $z^n$ = $\cos n\theta$ + i$\sin n\theta$ )

|$\sqrt{w}$| = 1

Hence, option B is correct.