Let \(a_1,a_2,\dots,a_n \)be the \(n^\text{th}\)roots of unity and let be the roots of unity. Compute \( \frac{a_1a_2\cdots a_n}{b_1b_2\cdots b_{n+1}}. \)
The hint is: What is the \(n^\text{th}\)root of unity?
Using Demoivre's Theorem, I found that the answer is i.