Mathematics 9709 · AS & A Level · Complex numbers

Complex numbers — practice question

For this question, you must not use a calculator. The complex numbers $w$ and $z$ satisfy the relation $w = \frac{z + i}{iz + 2}$.
(i)[4]

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

(ii)[4]

If instead $w = z$ and the real part of $z$ is negative, determine $z$, writing 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: Put $z=1+i$ into the formula and get $w=\frac{1+2i}{1+i}$

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