bearing in mind that complex roots, do not come all by their lonesome, the zeros of "-i" or "0-i" and "-7+i" aren't here all by themselves, they came with their sister, the conjugate
so, that is 0-i also comes with 0+i
and -7+i also comes with -7-i
so, the zeros, or solutions or roots, are [tex]\bf \begin{cases}
x=-1\implies &x+1=0\\
x=-i\implies &x+i=0\\
x=+i\implies &x-i=0\\
x=-7+i\implies &x+7-i=0\\
x=-7-i\implies &x+7+i=0
\end{cases}\\\\
-----------------------------\\\\
(x+1)(x+i)(x-i)(x+7-i)(x+7+i)=\textit{original polynomial}[/tex]
so, their product, is the 5th degree polynomial
