Is there any solution to this equation $1-2x\cos(\theta)+x^2=0$

Question

Is there any solution to this $1-2x\cos(\theta)+x^2=0$ and $1-2x^n\cos(n\theta)+x^{2n}$

I found this equation from the book Abraham de Moivre: Setting the stage for classical probability and its application. On page 65, the author states that the solution to this equation is $\cos(x)+i\sin(x)$ and $\cos(x)-i\sin(x)$. How do you derive the solutions?

Answer 1

You may easily figure the complex solutions of $$ (x^n-e^{ni\theta})(x^n-e^{-ni\theta}) = 0.$$