I am totally stuck on this problem. I need to find the cube roots of -8 in polar coordinates. I know that -8 lies on the real axis, so the angle of reference is $\displaystyle \pi$. I also know that $\displaystyle cos \pi=-1 $. I know that the formula I need to use is cube root of $\displaystyle |z|= cis \frac{\theta}{3}$ and I know that $\displaystyle cos \frac{\theta}{3}=Sqrt(\frac{1+cos\theta}{3})$, $\displaystyle sin\theta=Sqrt(\frac{1-cos\theta}{3})$ and the cube root $\displaystyle =2(cos\frac{\theta}{3}+i sin\frac{\theta}3}$. I must be tired and doing something wrong with the signs or something. I keep getting a zero for the first term and I am pretty sure the answer is $\displaystyle 1+i \sqrt{3}$. Please help! Thanks!