Question

If $z_1,z_2$be two $nth$ roots of unity such that they represent two point $A,B$ in the Argand plane where $\angle AOB={60}^{\circ }$ and $O$ is the orgin then the positive integer $n$ is of the form

• A. $4k,kϵN$
• B. $4k+3,kϵN$
• C. $6k,kϵN$
• D. $6k+5,kϵN$

Answer 1

The correct option is C $6k,kϵN$

From above concept

Let consider $k=0$ for $z_1$

So second root will be in ${60}^{\circ }$

Thus $z_2=cos\frac{\pi }{3}+isin\frac{\pi }{3}$

Hence $\frac{\pi }{3}=\frac{2k\pi }{n}$

$\Rightarrow n=6k$