Question

Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree​ 5; ​ zeros: -1; −i; −7+i

Answer 1

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 $\bf \begin{cases} x=-1\implies &x+1=0\\ x=-i\implies &x+i=0\\ x=+i\implies &x-i=0\\ x=-7+i\implies &x+7-i=0\\ x=-7-i\implies &x+7+i=0 \end{cases}\\\\ -----------------------------\\\\ (x+1)(x+i)(x-i)(x+7-i)(x+7+i)=\textit{original polynomial}$

so, their product, is the 5th degree polynomial