Some -complex- sum

Algebra Level 5

z2m+z2m1+z2m2++z+1=0\large z^{2m}+z^{2m-1} + z^{2m-2} + \ldots+z+1=0

Let the roots of the equation above be z1,z2,,z2mz_1, z_2, \ldots, z_{2m} . Find the value of r=12m1zr1 \displaystyle\sum_{r=1}^{2m} \frac1{z_r-1} .

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