Is there a theorem related to the sum of the roots of a positive number?

For example, for any integer n=1,2,3.....N, and positive number $\displaystyle \lambda$, such that $\displaystyle \lambda _k=\left | \lambda \right |^{1/n}exp^{2\pi ik/n} ...... k=0,1,2....n$ are the nth roots of $\displaystyle \lambda$, what is the sum of the roots,

i.e. $\displaystyle \sum_{k=0}^{n-1}\lambda _k = ?$.

In other words, is there a closed form, and general solution for the sum of roots, i.e. $\displaystyle \left | \lambda \right |^{1/n}\sum_{k=0}^{n-1}exp^{2\pi ik/n}$