Finding roots in Polar representation of complex number with powers

Question

$(2Z+1)^6 = -1$

I have tried:

\begin{align}W^6 &= -1\\ &= e^{(pai/2+2pai*k)/6}\\ K &= {0..5}\end{align}

And I got 6 answers. What to do now?

Answer 1

$$(2z+1)^6=-1=e^{(2m+1)i\pi}$$ where $m$ is any integer

$$2z+1=e^{(2m+1)i\pi/6}$$ where $m\equiv0,1,2,3,4,5\pmod6$

Now use $e^{2iy}-1=\cos2y+i\sin2y-1=-2\sin^2y+2i\sin y\cos y=2i\sin y(\cos y+i\sin y)$