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Properties of Cube Root of a Complex Number

If ω is one...

Question

If $ω$ is one of the complex cube roots of unity, then $(1 - ω + ω^{2}) (1 + ω - ω^{2})$ is equal to

A

0

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B

4

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C

3 ω

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D

1

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Solution

The correct option is C $4$
$(1 - ω + ω^{2}) (1 + ω - ω^{2})$
$= (- 2 ω) (- 2 ω^{2})$
$= 4 ω^{3}$
$= 4$

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