Let z=(1−i√3)/2, then the value of... | Complex Numbers | JEE Main

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JEE Main 2021

26-08-2021 S1

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Let $z=\frac{1-i \sqrt{3}}{2}, i=\sqrt{-1}$. Then the value of $21+\left(z+\frac{1}{z}\right)^3+\left(z^2+\frac{1}{z^2}\right)^3+\left(z^3+\frac{1}{z^3}\right)^3+\ldots+\left(z^{21}+\frac{1}{z^{21}}\right)^3$ is $\_\_\_\_$ .

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