[tex]\bf \textit{recalling that }~\hfill i^4=1~\hfill i^3=-i~\hfill i^2=-1 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 5i^4+2i^3+8i^2+\sqrt{-4}\implies 5(1)+2(-i)+8(-1)+\sqrt{-1\cdot 4} \\\\\\ 5-2i-8+\sqrt{-1}\cdot \sqrt{2^2}\implies -2i-3+i\cdot 2\implies ~~\begin{matrix} -2i \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~-3~~\begin{matrix} +2i \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill -3+0i~\hfill[/tex]
