Let $z=1+ai$ be a complex number, $a > 0$, such that $z^3$ is a real number. Then the sum $1+z+z^2+.....+z^{11}$ is equal to :

Question

$\begin{array}{1 1}(1)\; 1250 \sqrt{3} i \\ (2)\; 1250 \sqrt3 i \\ (3)\; 1365 \sqrt3 i \\(4)\; 1365 \sqrt3 i \end{array} $