[tex]x^4+ix^2+x+i | \underline{x+1}\\ \underline{-x^4-x^3} \ \ \ \ \ \ \ \ \ |x^3-x^2+(i+1)x-i\\ /-x^3+ix^2\\ . \ \ \ \ \underline{x^3+x^2}\\ . \ \ \ \ \ / \ (i+1)x^2+x\\ . \ \ \ \ \ \ \underline{ -(i+1)x^2-(i+1)x}\\. \ \ \ \ \ \ \ \ / \ \underline{x(1-i-1)+i} = \\ . \ \ \ \ \ \ \ \ \ -ix+i\\ . \ \ \ \ \ \ \ \ \ \ \underline{ix+i \ \ \ \ }\\ .\ \ \ \ \ \ \ \ \ \ / \ \ 2i \\\\\\ x^4+ix^2+x+i \ : \ x+1 = x^3-x^2+(i+1)x-i \ \ \hbox{rest} \ 2i[/tex]
