Gọi ${{z}_{1}},{{z}_{2}}$ là các nghiệm phức của phương trình...

Ta có: \)">{{z}^{2}}+z+1=0\Leftrightarrow \left[ \begin{aligned}
& {{z}_{1}}=\dfrac{-1+\sqrt{3}i}{2} \\
& {{z}_{2}}=\dfrac{-1-\sqrt{3}i}{2} \\
\end{aligned} \right.{{z}_{1}}=\dfrac{-1+\sqrt{3}i}{2}\Rightarrow z_{1}^{3}=1\Rightarrow {{\left( z_{1}^{3} \right)}^{673}}={{1}^{673}}\Rightarrow z_{1}^{2019}=1\Rightarrow z_{1}^{2021}=z_{1}^{2}=\dfrac{-1-\sqrt{3}i}{2}{{z}_{2}}=\dfrac{-1-\sqrt{3}i}{2}\Rightarrow z_{2}^{3}=1\Rightarrow {{\left( z_{2}^{3} \right)}^{673}}={{1}^{673}}\Rightarrow z_{2}^{2019}=1\Rightarrow z_{2}^{2021}=z_{2}^{2}=\dfrac{-1+\sqrt{3}i}{2}\text{w}=z_{1}^{2021}+z_{2}^{2021}=\dfrac{-1-\sqrt{3}i}{2}+\dfrac{-1+\sqrt{3}i}{2}=-1$.