Question

Find the missing term. If y = 1 + i, then y3 − 3y2 + ( ? ) − 1 = -i .

Answer 1

third choice is the answer

Answer 2

`y=1+i\qquad\qquad i^2=-1\\\\\\ y^3-3y^2+(?)-1 =-i\\\\(1+i)^3-3\cdot(1+i)^2+(?)-1+i=0\\\\1^3+3i+3i^2+i^3-3\cdot(1^2+2i+i^2)+(?)-1+i=0\\\\ 1+3i+3\cdot(-1)+i\cdot i^2-3-6i-3i^2+(?)-1+i=0\\\\ 1+3i-3+i\cdot(-1)-3-6i-3\cdot(-1)+(?)-1+i=0\\\\ 1+3i-3-i-3-6i+3+(?)-1+i=0\\\\ -3-3i+(?)=0\\\\(?)=3+3i\\\\(?)=3(1+i)\\\\\boxed{(?)=3y}`