$a\in\mathbb C$ such that $a^n=1,a^m\neq 1\,(m=1,2,\ldots,n-1) $ I would appreciate if somebody could help me with the following problem
Q: Suppose $a\in\mathbb C $ is a complex number such that: 
$$a^n=1,a^m\neq 1\,(m=1,2,\ldots,n-1) $$
find the value of:
$$\sum_{k=1}^{n-1}\ln|1-a^k| $$

In other words, $a$ is a primitive $n$th root of unity. Then
$$
\sum_{k=1}^{n-1}\ln|1-a^k|=\ln\left|\prod_{i=1}^{n-1}(1-a^k)\right|=\ln\left|1^{n-1}+\ldots+1^1+1^0\right|,
$$
because $\prod_{k=1}^n(x-a^k)=x^n-1$.
