The n^{th} roots of unity are in | vedclass

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(B) The equation for the $n^{th}$ roots of unity is given by $x^n = 1$. We can write $1$ in polar form as $\cos(2r\pi) + i\sin(2r\pi) = e^{i2r\pi}$ fo

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$G.P.$

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(B) The equation for the $n^{th}$ roots of unity is given by $x^n = 1$. We can write $1$ in polar form as $\cos(2r\pi) + i\sin(2r\pi) = e^{i2r\pi}$ for $r = 0, 1, 2, \dots, n-1$. Thus,the roots are $x = e^{i(2r\pi/n)}$. Substituting values of $r$,the roots are $1, e^{i(2\pi/n)}, e^{i(4\pi/n)}, \dots, e^{i(2(n-1)\pi/n)}$. These terms form a geometric progression $(G.P.)$ with the first term $a = 1$ and common ratio $r = e^{i(2\pi/n)}$.

The $n^{th}$ roots of unity are in

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