Moderate -0.8 This is a straightforward Argand diagram shading question requiring only direct application of three standard loci definitions (modulus circle, vertical line for real part, and argument rays). No calculation or problem-solving is needed—students simply identify and shade the intersection of three basic regions, making it easier than average.
2 On a sketch of an Argand diagram shade the region whose points represent complex numbers \(z\) satisfying the inequalities \(| z | \leqslant 3 , \operatorname { Re } z \geqslant - 2\) and \(\frac { 1 } { 4 } \pi \leqslant \arg z \leqslant \pi\).
For the vertical line and the circle, allow the B1 marks if all you see is the relevant part
Total
4
## Question 2:
| Answer | Marks | Guidance |
|--------|-------|----------|
| Show a circle with radius 3 and centre the origin | B1 | |
| Show the line $x = -2$ | B1 | |
| Show the correct half line for $\frac{\pi}{4}$ | B1 | |
| Shade the correct region | B1 | For the vertical line and the circle, allow the B1 marks if all you see is the relevant part |
| **Total** | **4** | |
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2 On a sketch of an Argand diagram shade the region whose points represent complex numbers $z$ satisfying the inequalities $| z | \leqslant 3 , \operatorname { Re } z \geqslant - 2$ and $\frac { 1 } { 4 } \pi \leqslant \arg z \leqslant \pi$.
\hfill \mbox{\textit{CAIE P3 2022 Q2 [4]}}