Mathematics 9709 · AS & A Level · Complex numbers

Complex numbers — practice question

For this question, calculator use is not allowed. The complex numbers $w$ and $z$ satisfy the relation $w = \frac{z + i}{iz + 2}$.

(i)[4]

If $z = 1 + i$, determine $w$ and give your answer in the form $x + iy$, where $x$ and $y$ are real.

(ii)[4]

Now suppose that $w = z$ and that the real part of $z$ is negative. Find $z$, giving your answer in the form $x + iy$, where $x$ and $y$ are real.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Replace $z$ by $1+i$ to get $w=\frac{1+2i}{1+i}$” …