JEE Advance - Mathematics (1999 - No. 15)
$$If\,i = \sqrt { - 1} ,\,\,then\,\,4 + 5{\left( { - {1 \over 2} + {{i\sqrt 3 } \over 2}} \right)^{334}} + 3{\left( { - {1 \over 2} + {{i\sqrt 3 } \over 2}} \right)^{365}}$$ is equal to
$$1 - i\sqrt 3 $$
$$ - 1 + i\sqrt 3 $$
$$i\sqrt 3 $$
$$ - i\sqrt 3 $$