$\begin{array}{l}
4{x^3} + 4x = 0 \Leftrightarrow 4x\left( {{x^2} + 1} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x = 0\\
{x^2} + 1 = 0
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = 0\\
{x^2} = - 1 = {i^2}
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = 0\\
x = i\\
x = - i
\end{array} \right.\\
\Rightarrow x = 0\,\,la\,\,nghiem\,\,boi\,\,1,\,\,\,k\,\,\,phai\,\,la\,\,nghiem\,\,kep.\\
i\,\,la\,\,don\,\,vi\,\,\,ao\,\,trong\,\,tap\,\,\,so\,\,phuc\,\,\,thoa\,\,\,man\,\,\,{i^2} = - 1.\,\,
\end{array}$