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Q

BITSAT If 1, w, w^2 are the cube roots of unity, the the value of

(1+\omega^{2}-\omega)(1-\omega^{2}+\omega) is

  1. 4

  2. \omega

  3. 2

  4. Zero

Answers (1)
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With the help of 2 properties of cube roots of unity, we can solve this question.

Property 1, \omega ^{3} = 1

Property 2, 1+ \omega +\omega ^{2} = 0

Now we have to find the value of (1+\omega^{2}-\omega)(1-\omega^{2}+\omega)

Using property 2, (-\omega -\omega )(-\omega ^{2} - \omega ^{2}) = (-2\omega )(-2\omega ^{2}) = 4\omega ^{3}

Now use property 1,

4\omega ^{3} = 4

Option (1) is correct

 

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