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Complex Numbers question

2023 · 24 Jan · Shift 2 · Q34

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JEE Main
Mathematics
Complex Numbers
2023 · 24 Jan · Shift 2 · Q34

Complex Numbers question

2023 · 24 Jan · Shift 2 · Q34

JEE MainMathematicsComplex NumbersMCQ+4 / −1

The value of

{\left( {{{1 + \sin {{2\pi } \over 9} + i\cos {{2\pi } \over 9}} \over {1 + \sin {{2\pi } \over 9} - i\cos {{2\pi } \over 9}}}} \right)^3}

is

A
$- {1 \over 2}\left( {1 - i\sqrt 3 } \right)$
B
$- {1 \over 2}\left( {\sqrt 3 - i} \right)$
C
${1 \over 2}\left( {1 - i\sqrt 3 } \right)$
D
${1 \over 2}\left( {\sqrt 3 + i} \right)$

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