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. \(\displaystyle \left | \lambda \right |^{1/n}\sum_{k=0}^{n-1}exp^{2\pi ik/n}\)