| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2020 |
| Session | December |
| Marks | 5 |
| Topic | Complex Numbers Argand & Loci |
| Type | Optimization of argument on loci |
| Difficulty | Moderate -0.3 This is a straightforward locus question requiring recognition that the equation represents a circle with center (-4, 4) and radius 2√2, followed by finding the arguments of the two tangent lines from the origin. The geometric setup is standard and the calculation involves basic trigonometry with no novel insight required, making it slightly easier than average. |
| Spec | 4.02k Argand diagrams: geometric interpretation4.02o Loci in Argand diagram: circles, half-lines |
Sketch on an Argand diagram the locus of all points that satisfy $|z + 4 - 4i| = 2\sqrt{2}$ and hence find $\theta, \phi \in (-\pi, \pi]$ such that $\theta \leq \arg z \leq \phi$. [5]
\hfill \mbox{\textit{SPS SPS FM 2020 Q9 [5]}}