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Complex Numbers question

2021 · 26 Aug · Shift 1 · Q34

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JEE Main
Mathematics
Complex Numbers
2021 · 26 Aug · Shift 1 · Q34

Complex Numbers question

2021 · 26 Aug · Shift 1 · Q34

JEE MainMathematicsComplex NumbersNumerical+4 / −1

Let

z = {{1 - i\sqrt 3 } \over 2}

,

i = \sqrt { - 1}

. Then the value of

21 + {\left( {z + {1 \over z}} \right)^3} + {\left( {{z^2} + {1 \over {{z^2}}}} \right)^3} + {\left( {{z^3} + {1 \over {{z^3}}}} \right)^3} + .... + {\left( {{z^{21}} + {1 \over {{z^{21}}}}} \right)^3}

is

\underline{\hspace{2cm}}

.

Numerical answer

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