If $\omega=\cos\large\frac{\pi}{n}$$+i\sin\large\frac{\pi}{n}$,then the value of $1+\omega+\omega^2+.....+\omega^{n-1}$ is :

Question

$\begin{array}{1 1}(A)\;1+i\\(B)\;1+i\tan(\large\frac{\pi}{n})\\(C)\;1+i\cot(\large\frac{\pi}{2n})\\(D)\;1+i\cot(\large\frac{\pi}{n})\end{array} $