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nth Root of a Complex Number

If 1, ω, ω2 a...

Question

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

A

1

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B

2

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C

3

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D

4

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Solution

The correct option is D $4$
Since $1, ω, ω^{2}$ are cube roots of unity,
$1 + ω + ω^{2} = 0 and ω^{3} = 1$
$Now, (1 - ω + ω^{2}) (1 + ω - ω^{2})$
$= (- ω - ω) (- ω^{2} - ω^{2})$
$= (- 2 ω) (- 2 ω^{2})$
$= 4 ω^{3} = 4$

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