Mathematics 9709 · AS & A Level · Complex numbers

Complex numbers — practice question

Let the complex number $1 + (\sqrt{2})i$ be represented by $u$. Let the polynomial $x^4 + x^2 + 2x + 6$ be represented by $p(x)$.

(a(i))[4]

With working shown, confirm that $u$ is a root of the equation $p(x) = 0$, and state another complex root of the equation.

(a(ii))[6]

Find the other two roots of the equation $p(x) = 0$.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Put in $x=1+\sqrt2 i$ and expand the powers.” …