x $ ^6+1=0 \\ \; \\ \therefore x^6 \;=\; -1 \;=\; cos\pi \;+\; isin\pi \\ \; \\ In \; General,\; x^6 \;=\; cos⁡(2n\pi+\pi)+isin⁡(2n\pi+\pi) \\ \; \\ \therefore x \;=\; [ cos⁡(2n\pi+\pi)+isin⁡(2n\pi+\pi) ]^{\dfrac{1}{6}} \\ \; \\ Applying \; De\; Moivre's \; Theorem, \\ \; \\ \;\\ \therefore x=cos⁡(\dfrac{2n+1}{6})\pi+isin(\dfrac{2n+1}{6}), \\ \; \\ where \; n=0,1,2,3,4,5 \\ \; \\ \; \\ \therefore x_0=cos\dfrac{\pi}{6}+isin \dfrac{\pi}{6} =\dfrac{\sqrt{3}}{2} +i \dfrac{1}{2} \;, \\ \; \\ x_1=cos\dfrac{\pi}{2}+isin \dfrac{\pi}{2} \;=\; i \\ \; \\ , x_2=cos\dfrac{5\pi}{6}+isin \dfrac{5\pi}{6} \; = \; \dfrac{-\sqrt{3}}{2} +i \dfrac{1}{2}, \\ \; \\ , x_3=cos\dfrac{7\pi}{6}+isin \dfrac{7\pi}{6} \;=\; \dfrac{-\sqrt{3}}{2} -i \dfrac{1}{2} \\ \; \\ , x_4=cos\dfrac{3\pi}{2}+isin \dfrac{3\pi}{2} \;=\; -i \\ \; \\ , x_5=cos\dfrac{11\pi}{6}+isin \dfrac{11\pi}{6} \; = \; \dfrac{\sqrt{3}}{2} -i \dfrac{1}{2} $