multiplying 3 variable a ,bi, cj

Question

I know how to do this $A × B = ( a + bi ) × ( c + di )$, but I don't understand how to do this $ A × B =( a + bi +cj) × ( d + ei +fj) =? $ I'm not sure how to group them or what to do with the i and the j as in this $+cj × ei$ Its for a fractal program im writing

Answer 1

Just distribute... $$(a+bi+cj)(d+ei+fj)=$$ $$(ad-be-cf)+(ae-bd)i+(af+cd)j+(bf-ce)k$$

We get the k terms since $$biej=beij=bek$$ And $$cjei=ceji=-cek$$