| Exam Board | WJEC |
|---|---|
| Module | Further Unit 1 (Further Unit 1) |
| Year | 2024 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Modulus-argument form conversions |
| Difficulty | Moderate -0.5 This is a straightforward modulus-argument conversion requiring division of complex numbers in Cartesian form, then converting to polar form. While it involves multiple steps (rationalizing the denominator, finding modulus and argument), these are standard Further Maths techniques with no conceptual difficulty or novel insight required. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02b Express complex numbers: cartesian and modulus-argument forms4.02e Arithmetic of complex numbers: add, subtract, multiply, divide4.02f Convert between forms: cartesian and modulus-argument |
\begin{enumerate}
\item The complex numbers $z , v$ and $w$ are related by the equation
\end{enumerate}
$$z = \frac { v } { w }$$
Given that $v = - 16 + 11 \mathrm { i }$ and $w = 5 + 2 \mathrm { i }$, find $z$ in the form $r ( \cos \theta + \mathrm { i } \sin \theta )$.\\
\hfill \mbox{\textit{WJEC Further Unit 1 2024 Q1 [5]}}