Answer :
Given the roots: 3,0,1,i,-i
We will write the equation for whose roots are
As we were given the roots, we can write the factors
so, we have the following factors:
[tex]\begin{gathered} x=3\rightarrow(x-3) \\ x=0\rightarrow x \\ x=1\rightarrow(x-1) \\ x=i\rightarrow(x-i) \\ x=-i\rightarrow(x+i) \end{gathered}[/tex]So, the equation will be:
[tex]f(x)=x(x-1)(x-3)(x-i)(x+i)[/tex]