## Roots of the equation x^n –1 = 0, n ∈I,

Q: Roots of the equation x^{n} –1 = 0, n ∈ I,

(A) are collinear (B) lie on a circle.

(C) form a regular polygon of unit circum-radius .

(D) are non-collinear.

Sol. Clearly, roots are 1, α, α^{2} , . . . α^{n-1} , where $\large \alpha = cos\frac{2\pi}{n} + i sin\frac{2\pi}{n}$ .

The distance of the complex numbers represented by these roots from origin is 1 i.e. all these points lie on a circle.

⇒ They are non-collinear.

⇒ They form a regular polygon of unit circum-radius.

Hence (B), (C) and (D) are the correct answers.