JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Easy

1 of 1

Application +4 | -1

1, \omega, \omega^2, \ldots \omega^{n-1}

are

n

, nth roots of unity, then the value of

(9-\omega)\left(9-\omega^2\right) \ldots . .\left(9-\omega^{n-1}\right)

will be

View answer and explanation

Correct option: C

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

Option C,

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

, is correct because it is derived by substituting

x=9

into the factored form of

x^n - 1

divided by

x-1

, where the roots of unity are used.

More Questions from COMPLEX NUMBERS

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{\left| {1 - i} \right|^x} = {2^x}

|z|=1

z \neq \pm 1

z, \frac{z}{1-z^2}

\left|z_r-r\right| \leq r, \forall r=1,2,3, \ldots, n

\left|\sum\limits_{r=1}^n z_r\right|

(z+a b)^3=a^3

a \neq 0

\alpha, \beta

\gamma

|\alpha-\beta|

{z^2} + {\left| z \right|^2} = 0,

z \in C

2x = - 1 + \sqrt 3 i

{\left( {1 - {x^2} + x} \right)^6} - {\left( {1 - x + {x^2}} \right)^6}