MathDB
Math Prize 2010 Problem 20

Source:

November 14, 2010
trigonometryalgebrapolynomialVietafunctionratiocomplex numbers

Problem Statement

What is the value of the sum ∑z1∣1−z∣2 , \sum_z \frac{1}{{\left|1 - z\right|}^2} \, , where zz ranges over all 7 solutions (real and nonreal) of the equation z7=−1z^7 = -1?
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