A Complex problem

Algebra Level 3

Let \(\{\phi_i\}_1^{n-1}\) denote the set of solutions to the equation : \[\sum_{k=0}^{n-1} \ z^k = 0, \quad where \ n >1 \ and \ \ z \in \mathbb C\]

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

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