Question 756890
Just some help but no further:


The needed set of zeros is 
{ 9, -i, +i, -8+i, -8-i }


The factored form is {{{f(x)=(x-9)(x-(-i))(x-(i))(x-(-8+i))(x-(-8-i))}}}
You have some multiplications and simplifications to do.  Avoid extra difficulties through careful pre-simplification and associating:
{{{f(x)=(x-9)(x+i)(x-i)(x+8-i)(x+8+i)}}}
{{{f(x)=(x-9)(x+i)(x-i)((x+8)-i)((x+8)+i)}}}
Continue the multiplications and simplifications.