| Exam Board | WJEC |
|---|---|
| Module | Further Unit 1 (Further Unit 1) |
| Session | Specimen |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Complex transformations and mappings |
| Difficulty | Standard +0.3 This is a standard Further Maths complex numbers locus problem requiring algebraic manipulation. Part (a) involves routine expansion of complex products and equating real/imaginary parts. Part (b) requires substitution and elimination to find a parabola equation—straightforward but multi-step. The techniques are well-practiced in Further Maths courses with no novel insight required. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02e Arithmetic of complex numbers: add, subtract, multiply, divide |
The complex numbers $z$ and $w$ are represented, respectively, by points $P(x, y)$ and $Q(u,v)$ in Argand diagrams and
$$w = z(1 + z)$$
\begin{enumerate}[label=(\alph*)]
\item Show that
$$v = y(1 + 2x)$$
and find an expression for $u$ in terms of $x$ and $y$. [4]
\item The point $P$ moves along the line $y = x + 1$. Find the Cartesian equation of the locus of $Q$, giving your answer in the form $v = au^2 + bu$, where $a$ and $b$ are constants whose values are to be determined. [5]
\end{enumerate}
\hfill \mbox{\textit{WJEC Further Unit 1 Q7 [9]}}