Question

lf $z_1$ and $z_2$ are two nth roots of unity, then $\arg \left(\frac{z_1}{z_2}\right)$ is a multiple of?

• A. $n\pi$
• B. $\frac{3\pi }{n}$
• C. $\frac{2\pi }{n}$
• D. $\frac{\pi }{n}$

Answer 1

The correct option is C $\frac{2\pi }{n}$

The nth roots of unity of a complex number z i.e. $z_1$, $z_2$, $z_3$,...and so on lies on a circle and the angle subtended by 2 consecutive roots is $\frac{2\pi }{n}$ . Please refer to the diagram (${\eta }_1$, ${\eta }_2$,... and so on can be assumed to be the roots) .