| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2025 |
| Session | February |
| Marks | 6 |
| Topic | Complex Numbers Argand & Loci |
| Type | Area calculations in complex plane |
| Difficulty | Challenging +1.2 This is a Further Maths complex numbers question requiring visualization of a circular region intersected by a vertical line, then calculating a circular segment area. It involves standard techniques (identifying circle center/radius, finding intersection points, using segment area formula) but requires careful geometric reasoning and exact form manipulation with surds and inverse trig, making it moderately above average difficulty. |
| 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 $\text{Re}(z) \geq 9$.
[6]
\hfill \mbox{\textit{SPS SPS FM 2025 Q7 [6]}}