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Polynomial Functions

Let P be no...

Question

Let $P$ be not multiple of $n$ and let $1, α, . . . . . . . α^{n - 1}$ be the $n^{t h}$ roots of unity. Then the value of $1 + α^{P} + . . . . . . + (α^{n - 1})^{P}$

A

0

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B

2 n

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C

n^{2}

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D

2 n^{2}

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Solution

The correct option is B $0$
Sum of n roots of unity $= 0$

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Similar questions

p

be an integer and let

1, α, \dots \dots α^{n - 1}

n^{th}

roots of unity. Then

1 + α^{p} + (α^{2})^{p} + \dots \dots + (α^{n - 1})^{p} =

p

be an integer and let

1, α, \dots \dots α^{n - 1}

n^{th}

roots of unity. Then

1 + α^{p} + (α^{2})^{p} + \dots \dots + (α^{n - 1})^{p} =

1, α, α^{2}, . . . . ., α^{n - 1}

n^{t h}

roots of unity, then

(1 - α) (1 - α^{2}) . . . . . (1 - α^{n - 1})

1, α, α^{2} . . . . . α^{n - 1}

are n roots of unity then ,

1. α . α^{2} . . . . α^{n - 1}

1, α_{1}, α_{2} α_{3} . . . . . . . . . . α_{n}_{-} 1

n^{t h}

roots of unity, then the value of

s i n \frac{π}{n}, s i n \frac{2 π}{n}, s i n \frac{3 π}{n} . . . . . . . . . . \frac{(n - 1) π}{n}

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