[tex]\bf (x^2+1)(x^3+2x)(x^2+4x-16i-4xi)=0\\\\
-------------------------------\\\\
x^2+1=0\implies x^2=-1\implies x=\sqrt{-1}\implies x=i\\\\
-------------------------------\\\\
x^3+2x=0\implies x(x^2+2)=0\implies
\begin{cases}
x=0\\
-------\\
x^2+2=0\\
x^2=-2\\
x=\sqrt{-2}\\
x=\sqrt{2\cdot -1}\\
x=\sqrt{2}\cdot \sqrt{-1}\\
x=i~\sqrt{2}
\end{cases}\\\\
-------------------------------\\\\[/tex]
[tex]\bf x^2+4x-16i-4xi=0\implies (x^2+4x)~-~(16i+4xi)=0
\\\\\\
(x^2+4x)~-~(4xi+16i)=0\implies x(x+4)~-~4i(x+4)=0
\\\\\\
\stackrel{common~factor}{(x+4)}(x-4i)=0\implies
\begin{cases}
x+4=0\\
x=-4\\
-----\\
x-4i=0\\
x=4i
\end{cases}[/tex]
