MathDB

20

Part of 2010 Math Prize For Girls Problems

Problems(1)

Math Prize 2010 Problem 20

Source:

11/14/2010
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?
trigonometryalgebrapolynomialVietafunctionratiocomplex numbers