If $1, w, w^{2}$ are three cube roots of unity, then $(1 - w + w^{2}) (1 + w - w^{2})$ is ____

1

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2

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3

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4

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Solution

The correct option is A $4$
If $1, w, w^{2}$ are three cube roots of unity, then $1 + ω + ω^{2} = 0$ ......(1)
Hence
$(1 - w + w^{2}) (1 + w - w^{2}) = (- ω - ω) (- ω^{2} - ω^{2})$ , use(1)
$= - 2 ω (- 2 ω^{2}) = 4 w^{3} = 4 (1) = 4$ , since $ω^{3} = 1$

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