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Mathematics · 2021

JEE Main · 26 August 2021, Shift 1 · Q89

Let z=(1-i √ 3)/2, i=√ -1. Then the value of 21+(z+1/z)^3+(z^2+1/z^2)^3+(z^3+1/z^3)^3+…+(z^21+1/(z^21))^3 is \ \ \ \.

Let $\displaystyle z=\frac{1-i \sqrt{3}}{2}, i=\sqrt{-1}$. 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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JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.