Standard +0.3 This is a straightforward loci question requiring students to identify and shade the intersection of a disc (center 3+i, radius 3) and a half-plane (perpendicular bisector condition). Both are standard A-level techniques with no novel problem-solving required, making it slightly easier than average.
3 On a sketch of an Argand diagram, shade the region whose points represent complex numbers \(z\) satisfying the inequalities \(| z - 3 - \mathrm { i } | \leqslant 3\) and \(| z | \geqslant | z - 4 \mathrm { i } |\).
Must be some evidence of scale on both axes or centre stated as \(3+i\) or \((3,1)\)
Show a circle with radius 3 and centre not at the origin
B1
Must be some evidence that radius \(=3\) or stated \(r=3\)
Show the line \(y=2\)
B1
Line \(y=2\) can be represented by 2 or correct dashes
Shade the correct region
B1
Line and circle must be correct
## Question 3:
| Answer | Mark | Guidance |
|--------|------|----------|
| Show a circle with centre $3+i$ | B1 | Must be some evidence of scale on both axes or centre stated as $3+i$ or $(3,1)$ |
| Show a circle with radius 3 and centre not at the origin | B1 | Must be some evidence that radius $=3$ or stated $r=3$ |
| Show the line $y=2$ | B1 | Line $y=2$ can be represented by 2 or correct dashes |
| Shade the correct region | B1 | Line and circle must be correct |
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3 On a sketch of an Argand diagram, shade the region whose points represent complex numbers $z$ satisfying the inequalities $| z - 3 - \mathrm { i } | \leqslant 3$ and $| z | \geqslant | z - 4 \mathrm { i } |$.
\hfill \mbox{\textit{CAIE P3 2023 Q3 [4]}}