Value of z satisfying the equation $\log z+\log z^2+.......+\log z^n=0$ is

Question

$\begin{array}{1 1}(A)\;\sin\large\frac{4m\pi}{n}\normalsize +i\cos\large\frac{4m\pi}{n}\normalsize ,m=1,2....\\(B)\;\cos\large\frac{4m\pi}{n(n+1)}\normalsize -i\sin\large\frac{4m\pi}{n(n+1)}\normalsize ,m=1,2....\\(C)\;\cos\large\frac{4m\pi}{n(n+1)}\normalsize +i\sin\large\frac{4m\pi}{n(n+1)}\normalsize ,m=1,2....\\(D)\;0\end{array} $