Question 141517
Both complex and irrational roots come in conjugate pairs.  That is, if you have a root of the form {{{a+bi}}}, there must also be a root {{{a-bi}}}.  Likewise, if {{{a+sqrt(b)}}} is a root, then {{{a-sqrt(b)}}} is also a root.


Your roots are in these forms because {{{-8i=0-8i}}} and {{{sqrt(8)=0+sqrt(8)}}}


A number {{{alpha}}} is a zero of a polynomial function if and only if {{{x-alpha}}} is a factor of the polynomial, so:


{{{(x-8i)(x+8i)(x-sqrt(8))(x+sqrt(8))}}} are the factors of your minimum (4th) degree polynomial.  So get busy multiplying.