If 1- - -2- -n - 1 are n- nth roots of unity- then the value of 9 - - - 9 - -2 - 9 - -3 - 9 - -n - 1 will be

The correct option is B 9^n 18 Let x = (1)^1/n ⇒ x^n 1 = 0 or x^n 1 = (x 1)(x ω)(x ω^2) ....(x ω^n 1) ⇒x^n 1x 1 = ...

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Particular Solution of a Differential Equation

If 1, ω, ω2...

Question

If $1, ω, ω^{2}, . . . . ω^{n - 1}$ are $n, n^{t h}$ roots of unity, then the value of
$(9 - ω) \cdot (9 - ω^{2}) \cdot (9 - ω^{3}) . . . (9 - ω^{n - 1})$ will be

\frac{9^{n} + 1}{8}

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9^{n} - 1

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\frac{9^{n} - 1}{8}

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9^{n} + 1

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Solution

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Similar questions

ω, ω^{2}, ω^{3}, . . . . . . . . ω^{n - 1}

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

1, ω, ω^{2}, ω^{3} . . . . ., ω^{n - 1}

n^{t h}

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

1, ω, ω^{2}, ω^{3} . . . . ., ω^{n - 1}

n^{t h}

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

1, ω, ω^{2}, . . ., ω^{n - 1}

n^{t h}

(5 - ω) (5 - ω^{2}) . . . (5 - ω^{n - 1}) =

1, ω, ω^{2}, \dots, ω^{n - 1}

n^{th}

x^{n} = 1.

(5 - ω) (5 - ω^{2}) \dots (5 - ω^{n - 1})

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