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

Question

$ - {1 \over 2}\left( {1 - i\sqrt 3 } \right)$

$ - {1 \over 2}\left( {\sqrt 3 - i} \right)$

${1 \over 2}\left( {1 - i\sqrt 3 } \right)$

${1 \over 2}\left( {\sqrt 3 + i} \right)$

Solution

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