[tex]x^3=i^3\\\\x^3-i^3=0\\\\(x-i)(x^2+xi-1)=0\\\\x=i\\\\\\\x^2+xi-1=0\\\\\Delta=i^2-4\cdot1\cdot(-1)=-1+4=3\\\\\sqrt{\Delta}=\sqrt3 \\\\x_1=\dfrac{-i-\sqrt3}{2}=-\dfrac{\sqrt3}{2}-\dfrac{1}{2}i\\\\x_2=\dfrac{-i+\sqrt3}{2}=\dfrac{\sqrt3}{2}-\dfrac{1}{2}i\\\\\\\boxed{x\in\left\{i,-\dfrac{\sqrt3}{2}-\dfrac{1}{2}i,\dfrac{\sqrt3}{2}-\dfrac{1}{2}i\right\}}[/tex]
