$\mathrm{If} {\mathrm{x}}^6+1=0, \mathrm{then} \mathrm{x}=$

$\begin{array}{rcl}{\mathrm{x}}^6+1& =& 0\\ {\mathrm{x}}^6& =& -1\\ {\mathrm{x}}^6& =& \cos \mathrm{\pi }+\mathrm{i} \sin \mathrm{\pi }\\ \mathrm{x}& =& {\left(\cos \mathrm{\pi }+\mathrm{i} \sin \mathrm{\pi }\right)}^{\frac{1}{6}}\\ \mathrm{x}& =& \cos \frac{2\mathrm{k\pi }+\mathrm{\pi }}{6}+\mathrm{i} \sin \frac{2\mathrm{k\pi }+\mathrm{\pi }}{6}, \mathrm{k}=0, 1. 2, 3, 4, 5\\ \mathrm{x}& =& \mathrm{cis} \frac{(2\mathrm{k}+1)\mathrm{\pi }}{6} : \mathrm{k}=0, 1, 2, 3, 4, 5.\end{array}$