MHT CET · Maths · Complex Number
If \(\alpha\) and \(\beta\) are the complex cube roots of unity, then \(\alpha^3+\beta^3+\alpha^{-2} \times \beta^{-2}\) is equal to
- A \(1\)
- B \(-3\)
- C \(3\)
- D \(0\)
Answer & Solution
Correct Answer
(C) \(3\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \alpha^3+\beta^3+\alpha^{-2} \cdot \beta^{-2}=\alpha^3+\beta^3+\frac{1}{\alpha^2 \beta^2} \\ & =\omega^3+\omega^6+\frac{1}{\omega^2 \omega^4}=1+1+1=3\end{aligned}\)
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