If z 2 + z + 1 = 0, where z is a complex number, then the value of (z+ 1 z )^ 2 + (z^ 2 +…
Mathematics · JEE Advanced · NTA Exams — Complex Numbers and Quadratic Equations
If z2 + z + 1 = 0, where z is a complex number, then the value of \(\left(z+\frac{1}{z}\right)^{2}+\left(z^{2}+\frac{1}{z^{2}}\right)^{2}\)\(+\left(z^{3}+\frac{1}{z^{3}}\right)^{2}+\ldots+\left(z^{6}+\frac{1}{z^{6}}\right)^{2} \text { is }\)
- \(18\)
- \(54\)
- \(12\)
- \(6\)
Answer
(C) 12
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