What is the smallest positive integer \(n\) such that all the roots of \(z^4 - z^2 + 1 = 0\) are \(n^{\text{th}}\) roots of unity?
Thanks a lot! :)
Using exponential form, we can express the roots as e^(2*pi*i/18), e^(2*3*pi*i/18), e^(2*11*pi*i/18), and e^(2*17*pi*i/18). Therefore, the smallest n that works is 18.