Problem 5

(Problem posed by Nagendra P (University of Mysore) and Yathirajsharma (Sarada Vilas))

Let \(\omega=e^{\frac{2i\pi}{7}}\) be a seventh root of unity i.e one of the solutions of the equation \(z^7-1=0\). Find the value of

\(\omega+\omega^2-\omega^3+\omega^4-\omega^5-\omega^6\)

(Comment the value in the comment box and send the detailed solution to dep.math.svc@gmail.com on or before 30th of June, 2023.)