Solving $z^5=-16+16\sqrt3i$ using the fifth roots of unity 
1 Write down the fifth roots of unity. Hence, or otherwise, find all the roots of the equation
  $$z^5=-16+16\sqrt3i,$$
  giving each root in the form $re^{i\theta}$. [4]

In this question, I can work out the answer using de Moivre's theorem, but the question implies that I have to use the 5 roots of unity somehow. Does it just mean that I have to solve the equation in the same way as I solved it for the 5 roots of unity, or whether I have to actually use the 5 roots of unity?

From $z^5=-16+16\sqrt3i$ we have $(\frac z {\sqrt[5]32})^5=\frac {-1} 2+ \frac {\sqrt3i} 2$ and $(\frac z 2)^5=\frac {-1} 2+ \frac {\sqrt3i} 2= \cos \frac {\pi} 3 + i \sin \frac {\pi} 3= (\cos \frac {\pi} {15} + i \sin \frac {\pi} {15})^5$
Now making a notation $u=\frac {z}{2(\cos \frac {\pi} {15} + i \sin \frac {\pi} {15})}$ we get $u^5 = 1$
