How to solve $x^3=-1$? How to solve $x^3=-1$? I got following: 
$x^3=-1$ 
$x=(-1)^{\frac{1}{3}}$
$x=\frac{(-1)^{\frac{1}{2}}}{(-1)^{\frac{1}{6}}}=\frac{i}{(-1)^{\frac{1}{6}}}$...

$$x^3=-1$$
$$x^3+1=0$$
$$(x+1)(x^2+1-x)=0$$
$$x=-1 \quad\text{or}\quad x^2-x+1=0$$
When $$x^2-x+1=0, x= \frac{-1(\pm\sqrt{-3})}{2}$$
$$x= \frac{-1+\sqrt{3}i}{2} \quad\text{and}\quad \frac{-1-\sqrt{3}i}{2}$$
Which is equal to $e^{−i2π/3}$ and $e^{i2π/3}$ respectively. 
