If 1, , ^2, ¹⁰ are 11 th roots of unity, then product of these roots is 1

Step-by-step solution

Given 1, , ^2, , ¹⁰ are 11 th roots of unity. 1, , ^2, , ¹⁰ are the roots of the equation given below. or aligned & x=(1)^ 1 / 11 or & x¹¹=1 & x¹¹-1=0 & aligned Since, we know that product of roots of a polynomial of degree n=(-1)^n Constant term Coefficient of x^n 1 ^2 ¹⁰= (-1)¹¹(-1) 1 =1