| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2022 |
| Session | February |
| Marks | 8 |
| Topic | Complex Numbers Arithmetic |
| Type | Division plus other arithmetic operations |
| Difficulty | Moderate -0.8 This is a straightforward complex number manipulation question testing basic operations (linear combinations, powers, division). All three parts are routine calculations requiring only direct application of standard techniques with no problem-solving or insight needed. While it's Further Maths content, these are foundational complex number skills that are more computational than conceptual, making it easier than average. |
| Spec | 4.02e Arithmetic of complex numbers: add, subtract, multiply, divide |
The complex numbers $3 - 2i$ and $2 + i$ are denoted by $z$ and $w$ respectively. Find, giving your answers in the form $x + iy$ and showing clearly how you obtain these answers,
\begin{enumerate}[label=(\roman*)]
\item $2z - 3w$, [2]
\item $(iz)^2$, [3]
\item $\frac{z}{w}$. [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2022 Q2 [8]}}