If omega is an n^{th} root of unity,other tha | vedclass

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(A) The expression $1 + \omega + \omega^2 + ... + \omega^{n-1}$ is a geometric progression with $n$ terms,where the first term $a = 1$ and the common

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(A) The expression $1 + \omega + \omega^2 + ... + \omega^{n-1}$ is a geometric progression with $n$ terms,where the first term $a = 1$ and the common ratio is $\omega$.The sum of a geometric progression is given by $S_n = \frac{a(r^n - 1)}{r - 1}$.Substituting $a = 1$ and $r = \omega$,we get $S_n = \frac{\omega^n - 1}{\omega - 1}$.Since $\omega$ is an $n^{th}$ root of unity,$\omega^n = 1$.Therefore,$S_n = \frac{1 - 1}{\omega - 1} = \frac{0}{\omega - 1} = 0$ (given $\omega 
eq 1$).

If $\omega$ is an $n^{th}$ root of unity,other than unity,then the value of $1 + \omega + \omega^2 + ... + \omega^{n-1}$ is

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