Set this up to FOIL the 2 sets of factors. They are [x-(-1+i)][x-(-1-i)] which simplify down to, after distributing the negative into each set of parenthesis: (x+1-i)(x+1+i). FOIL these using inner first, outer last. Doing that gives us [tex] x^{2} +x+ix+x+1+i-ix-i- i^{2} [/tex]. Let's put that into some order so we can see what cancels out. [tex] x^{2} +x+x+ix-ix+i-i+1- i^{2} [/tex]. After the canceling, we are left with [tex] x^{2} +2x+1- i^{2} [/tex]. Since [tex] i^{2} =-1[/tex], we now have [tex] x^{2} +2x+1-(-1)[/tex] which of course simplifies to [tex] x^{2} +2x+1+1[/tex] or [tex] x^{2} +2x+2[/tex]. Therefore, your missing term is 2x. Phew!!!
