I am assuming you mean the twelve twelveth roots of unity?.
Writing \(\displaystyle 1=cos(0)+isin(0)\) and use the theorem on nth roots.
we get \(\displaystyle w_{k}=cos(\frac{2{\pi}k}{12})+isin(\frac{2{\pi}k}{12})\)
For k=0, \(\displaystyle cos(0)+isin(0)=1\)
For k=1, \(\displaystyle cos(\frac{2{\pi}}{12})+isin(\frac{2{\pi}}{12})=\frac{\sqrt{3}}{2}+\frac{1}{2}i\)
For k=2, \(\displaystyle cos(\frac{4{\pi}}{12})+isin(\frac{4{\pi}}{12})=\frac{1}{2}+\frac{\sqrt{3}}{2}i\)
And so on, clean up to k=11.
