Mathematics 9709 · AS & A Level · Complex numbers

Complex numbers — practice question

(a)[3]

On an Argand diagram, shade the set of points representing complex numbers $z$ that satisfy the inequalities $-\frac{1}{3}\pi \leq \arg(z - 1 - 2i) \leq \frac{1}{3}\pi$ and $\Re z \leq 3$.

(b)[2]

Calculate the minimum value of $\arg z$ for points in the region from part (a). Give your answer in radians correct to 3 decimal places.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: Draw the correct half-lines from $1+2i$, arranged symmetrically about $y=2i$, and lying between $\frac{\pi}{4}$ and $\frac{5\pi}{12}$.

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