How do I find the three cube roots of unity?
Although you could use de Moivre's Threorem, or another version of the geometry of the complex plane, it's not needed if you know and apply some algebra:
The cube roots on unity (1) are the complex solutions to
Method 1: use
Method 2: Use the (obvious?) fact that
Then do the division (long or synthetic) (or use trial and error) to get
So we need to solve:
Use your favorite applicable method to solve: