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Properties of nth Root of a Complex Number

If α and ...

Question

If $α$ and $β$ are the roots of $x^{2} - x + 1 = 0$ , then the value of $α^{2013} + β^{2013}$ is equal to

A

2

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B

- 2

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C

- 1

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D

1

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Solution

The correct option is A $- 2$
$α = - ω, - ω^{2}$
$⟹ - ω^{2013} - ω^{2 \times 2013}$
$= - (ω^{3})^{671} - (ω^{3})^{2 \times 671} = - 2$

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