Standard +0.3 This is a standard Argand diagram region question requiring interpretation of two inequalities: a perpendicular bisector (from the modulus inequality) and an angular sector (from the argument inequality). While it requires understanding of loci concepts, the techniques are routine for P3/Further Pure—students identify the perpendicular bisector of points 2i and -2+i, then shade the intersection with a 45° sector from -1. This is slightly easier than average as it's a direct application of standard loci without requiring algebraic manipulation or proof.
2 On an Argand diagram, shade the region whose points represent complex numbers \(z\) satisfying the inequalities \(| z - 2 \mathrm { i } | \leqslant | z + 2 - \mathrm { i } |\) and \(0 \leqslant \arg ( z + 1 ) \leqslant \frac { 1 } { 4 } \pi\).
Can be implied if the correct perpendicular is drawn
Show perpendicular bisector of their \((2i\) and \(-2+i)\)
B1FT
Show correct half-line of gradient 1 from point \((-1, 0)\)
B1
Should pass through \((0, 1)\)
Correct loci and shade correct region
B1
## Question 2:
| Answer | Marks | Guidance |
|--------|-------|----------|
| Show points representing $2i$ and $-2+i$ | B1 | Can be implied if the correct perpendicular is drawn |
| Show perpendicular bisector of their $(2i$ and $-2+i)$ | B1FT | |
| Show correct half-line of gradient 1 from point $(-1, 0)$ | B1 | Should pass through $(0, 1)$ |
| Correct loci and shade correct region | B1 | |
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