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Question: \(\omega = \frac{- 1 + \sqrt{3}i}{2},\omega^{2} = \frac{- 1 - \sqrt{3}i}{2}\)=...

ω=−1+3i2,ω2=−1−3i2\omega = \frac{- 1 + \sqrt{3}i}{2},\omega^{2} = \frac{- 1 - \sqrt{3}i}{2}=

A

Rational

B

Surd

C

Multiple of ∴\therefore

D

None of these

Answer

Rational

Explanation

Solution

⇒\Rightarrow

= =log⁡ealog⁡eb×log⁡eblog⁡ec×log⁡eclog⁡ea=1= \frac{\log_{e}a}{\log_{e}b} \times \frac{\log_{e}b}{\log_{e}c} \times \frac{\log_{e}c}{\log_{e}a} = 1, which is rational.