Moderate -0.5 This is a straightforward loci question requiring students to sketch two standard regions: the exterior of a circle centered at the origin with radius 2, and the interior of a circle centered at (1,-1) with radius 1. It involves direct application of modulus 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 \(| z | \geqslant 2\) and \(| z - 1 + \mathrm { i } | \leqslant 1\).
The FT is on the position of \(1 - i\). Shaded region outside circle with centre the origin and radius 2 and inside circle with centre \(\pm 1 \pm i\) and radius 1
## Question 2:
| Answer | Marks | Guidance |
|--------|-------|----------|
| Show a circle with centre the origin and radius 2 | B1 | |
| Show the point representing $1 - i$ | B1 | |
| Show a circle with centre $1 - i$ and radius 1 | B1 FT | The FT is on the position of $1 - i$ |
| Shade the appropriate region | B1 FT | The FT is on the position of $1 - i$. Shaded region outside circle with centre the origin and radius 2 and inside circle with centre $\pm 1 \pm i$ and radius 1 |
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2 On a sketch of an Argand diagram, shade the region whose points represent complex numbers $z$ satisfying the inequalities $| z | \geqslant 2$ and $| z - 1 + \mathrm { i } | \leqslant 1$.
\hfill \mbox{\textit{CAIE P3 2020 Q2 [4]}}