# 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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