Question

Which of the following is incorrect regarding $n^{th}$ roots of unity?

• A. The number of distinct roots is $n$
• B. The roots are in G.P. with common ratio $c=\frac{2\pi }{n}$
• C. The arguments are in A.P. with common difference $\frac{2\pi }{n}$
• D. Product of the roots is $0$ and the sum of the roots is $\pm 1$

Answer 1

The correct option is D Product of the roots is $0$ and the sum of the roots is $\pm 1$

Consider $x^n=1$ , where $x$ is $n^{th}$ root of unity

Here in $x^n-1=0$ , the product of roots is $\pm 1$ and the sum of roots is $0$

Therefore option $D$ is incorrect