Some -complex- sum

Algebra Level 5

\[\large z^{2m}+z^{2m-1} + z^{2m-2} + \ldots+z+1=0\]

Let the roots of the equation above be \(z_1, z_2, \ldots, z_{2m} \). Find the value of \( \displaystyle\sum_{r=1}^{2m} \frac1{z_r-1} \).

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