(C) The $11^{th}$ roots of unity are the roots of the equation $x^{11} - 1 = 0$.By Vieta's formulas,for a polynomial equation $a_n x^n + a_{n-1} x^{n-

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(C) The $11^{th}$ roots of unity are the roots of the equation $x^{11} - 1 = 0$.By Vieta's formulas,for a polynomial equation $a_n x^n + a_{n-1} x^{n-1} + \ldots + a_0 = 0$,the product of the roots is given by $(-1)^n \cdot \frac{a_0}{a_n}$.Here,$n = 11$,$a_{11} = 1$,and $a_0 = -1$.Therefore,the product of the roots is $(-1)^{11} \cdot \frac{-1}{1} = (-1) \cdot (-1) = 1$.

Class 11 Mathematics 1 Complex Numbers and Quadratic Equations: Complex Numbers De Moivre's theorem and Roots of unity

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If $1, \omega, \omega^2, \ldots, \omega^{10}$ are the $11^{th}$ roots of unity,then the product of these roots is:

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A
$\omega$
B
$-1$
C
$1$
D
$\omega^2$

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1 Complex Numbers and Quadratic Equations: Complex Numbers

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De Moivre's theorem and Roots of unity

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