Let be a fifth root of unity

MATHEMATICS · Numerical · CBSE · Mathematics · Complex Numbers and Quadratic Equations · Complex Numbers and Quadratic Equations

Problem

Let α\alpha be a fifth root of unity, where α≠1\alpha\ne1. Find the value of α[1+∑k=1∞αk(1−α)(1−α2)⋯(1−αk)]\alpha\left[1+\sum_{k=1}^{\infty}\alpha^k(1-\alpha)(1-\alpha^2)\cdots(1-\alpha^k)\right].

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