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Properties of Cube Root of a Complex Number

If 1, ω, ω 2 ...

Question

If $1, ω, ω^{2}$ are the cube roots of unity, then their product is
[Karnataka CET 1999, 2001]

A

\N

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B

ω

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C

-1

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D

1

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Solution

The correct option is D 1
$1. ω . ω^{2} = ω^{3} = 1.$

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ω

is an n^th root of unity, other than unity, then the value of

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[Karnataka CET 1999]

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∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & ω^{n} & ω^{2 n} ω^{n} & ω^{2 n} & 1 ω^{2 n} & 1 & ω^{n} \end{matrix} ∣ ∣ ∣ ∣ ∣

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Properties of Cube Root of a Complex Number

Standard XIII Mathematics

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