Complex Solutions to Polynomial Equations I have to find another complex solution to the polynomial equation $z^6 - 1 = 0$ given that $\frac{1}{2}−\frac{\sqrt{3}}{2}i$ is a solution. 
I guess the question I have for this is that is there any other way other than expanding the brackets out completely? 

$$x^6-1=(x^3-1)(x^3+1)=(x-1)(x^2+x+1)(x+1)(x^2-x+1)$$
the roots are as follows
$$x_1=1$$
$$x_2=-1$$
roots of $x^2+x+1$ are
$$x_{3,4}=-\frac{1}{2}\pm \frac{\sqrt{3}i}{2}$$
roots of $x^2-x+1$ are
$$x_{5,6}=\frac{1}{2}\pm \frac{\sqrt{3}i}{2}$$
