Moderate -0.5 This is a straightforward Argand diagram shading question requiring identification of a disk (circle with radius 2 centered at -2+3i) intersected with a half-plane (argument ≤ 3π/4). It involves direct application of standard loci definitions with no problem-solving or novel insight required, making it slightly easier than average.
2 On a sketch of an Argand diagram, shade the region whose points represent complex numbers \(z\) satisfying the inequalities \(| z + 2 - 3 \mathrm { i } | \leqslant 2\) and \(\arg z \leqslant \frac { 3 } { 4 } \pi\).
Show a circle of radius 2 and centre not at the origin
B1
Show correct half line from the origin
B1
\(\frac{3\pi}{4}\) or \(\frac{\pi}{4}\) seen, or half line that approximately bisects angle \(\frac{\pi}{2}\)
Shade the correct region
B1
Total: 4
N.B. Maximum 3 out of 4 if any errors seen
## Question 2:
| Answer | Mark | Guidance |
|--------|------|----------|
| Show a circle with centre $-2 + 3i$ | B1 | Must see $(-2, 3)$ or appropriate marks on axes |
| Show a circle of radius 2 and centre not at the origin | B1 | |
| Show correct **half line** from the origin | B1 | $\frac{3\pi}{4}$ or $\frac{\pi}{4}$ seen, or half line that approximately bisects angle $\frac{\pi}{2}$ |
| Shade the correct region | B1 | |
| **Total: 4** | | N.B. Maximum 3 out of 4 if any errors seen |
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2 On a sketch of an Argand diagram, shade the region whose points represent complex numbers $z$ satisfying the inequalities $| z + 2 - 3 \mathrm { i } | \leqslant 2$ and $\arg z \leqslant \frac { 3 } { 4 } \pi$.
\hfill \mbox{\textit{CAIE P3 2022 Q2 [4]}}