JEE Mains · Maths · STD 11 - 4.1 complex nubers
If \(\alpha, \beta, \gamma, \delta\) are the roots of the equation \(x^{4}+x^{3}+x^{2}+x+1=0\), then \(\alpha^{2021}+\beta^{2021}+\gamma^{2021}+\delta^{2021}\) is equal to
- A \(-4\)
- B \(-1\)
- C \(1\)
- D \(4\)
Answer & Solution
Correct Answer
(B) \(-1\)
Step-by-step Solution
Detailed explanation
\(\alpha, \beta, \gamma, \delta\) root of the equation \(x^{4}+x^{3}+x^{2}+x+1=0\) Which are \(5^{\text {th }}\) roots of unity except \(1\). then \(\alpha^{2021}+\beta^{2021}+\gamma^{2021}+\delta^{2021}=\) \(\alpha+\beta+\gamma+\delta=-1\)
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