A Complex problem

Algebra Level 3

Let {ϕi}1n1\{\phi_i\}_1^{n-1} denote the set of solutions to the equation : k=0n1 zk=0,where n>1 and  zC\sum_{k=0}^{n-1} \ z^k = 0, \quad where \ n >1 \ and \ \ z \in \mathbb C

What is the value of k=1n1 ϕk \displaystyle \sum_{k=1}^{n-1} \ \phi_k ?

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