| Exam Board | WJEC |
|---|---|
| Module | Further Unit 1 (Further Unit 1) |
| Year | 2024 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Intersection of two loci |
| Difficulty | Standard +0.3 This is a standard Further Maths locus problem requiring identification of L₁ as a perpendicular bisector and L₂ as a circle, then solving simultaneous equations. The algebraic manipulation is straightforward with no conceptual surprises, making it slightly easier than average for Further Maths content. |
| Spec | 4.02k Argand diagrams: geometric interpretation4.02o Loci in Argand diagram: circles, half-lines |
\begin{enumerate}
\item The complex number $z$ is represented by the point $P ( x , y )$ in an Argand diagram.
\end{enumerate}
Two loci, $L _ { 1 }$ and $L _ { 2 }$, are given by:
$$\begin{aligned}
& L _ { 1 } : | z - 2 + \mathrm { i } | = | z + 2 - 3 \mathrm { i } | \\
& L _ { 2 } : | z - 2 + \mathrm { i } | = \sqrt { 10 }
\end{aligned}$$
(a) Find the coordinates of the points of intersection of these loci.\\
(b) On the same Argand diagram, sketch the loci $L _ { 1 }$ and $L _ { 2 }$. Clearly label the coordinates of the points of intersection.\\
\hfill \mbox{\textit{WJEC Further Unit 1 2024 Q6 [12]}}