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nth Root of a Complex Number

If ω is an nt...

Question

If $ω$ is an n^th root of unity, other than unity, then the value of $1 + ω + ω^{2} + . . . . + ω^{n - 1}$ is
[Karnataka CET 1999]

A

1

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B

-1

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C

None of these

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Solution

$1 + ω + ω^{2} + . . . . + ω^{n - 1} = (\frac{ω^{n} - 1}{ω - 1}) = 0, (∵ ω^{n} = 1)$

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[Karnataka CET 1999]

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