| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2023 |
| Session | February |
| Marks | 6 |
| Topic | Complex Numbers Argand & Loci |
| Type | Area calculations in complex plane |
| Difficulty | Challenging +1.2 This question requires visualizing a circle in the complex plane (center (5,2), radius √32) and finding the area of intersection with the half-plane Re(z) ≥ 9. Students must recognize the geometry, find the chord length using the perpendicular distance from center to line, then apply the circular segment area formula. While it involves multiple steps and coordinate geometry with complex numbers, the techniques are standard for Further Maths students and the setup is relatively straightforward once the geometry is identified. |
| Spec | 4.02k Argand diagrams: geometric interpretation4.02o Loci in Argand diagram: circles, half-lines |
Find, in exact form, the area of the region on an Argand diagram which represents the locus of points for which $|z - 5 - 2i| \leq \sqrt{32}$ and Re (z) $\geq$ 9. [6]
\hfill \mbox{\textit{SPS SPS FM 2023 Q11 [6]}}