Q.If A, B, C are angles of a triangle such that $x=\text{cis}A$, $y=\text{cis}B$, $z=\text{cis}C$, then find the value of $xyz$.

De Moivre's theorem states that $(\cos\theta + i\sin\theta)^n = \cos n\theta + i\sin n\theta$ for every integer $n$, and it extends (as a one-valued statement) to rational $n$ as well. It is the single tool that lets us raise a complex number to any power in one step and, run in reverse, lets us pull out every $n^{th}$ r …