| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2013 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Division plus other arithmetic operations |
| Difficulty | Easy -1.2 This is a straightforward complex number arithmetic question requiring only basic operations (subtraction and multiplication). Part (a) is trivial substitution, and part (b) involves simple distribution with i² = -1. Despite being Further Maths, this is a routine warm-up question testing fundamental definitions rather than problem-solving skills. |
| Spec | 4.02e Arithmetic of complex numbers: add, subtract, multiply, divide |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(z - w = \{(8+3i) - (-2i)\} = 8 + 5i\) | B1 | [1] |
| (b) \(zw = \{(8+3i)(-2i)\} = 6 - 16i\) | M1 A1 | Either the real or imaginary part is correct |
**(a)** $z - w = \{(8+3i) - (-2i)\} = 8 + 5i$ | B1 | [1]
**(b)** $zw = \{(8+3i)(-2i)\} = 6 - 16i$ | M1 A1 | Either the real or imaginary part is correct | [2]
**Total: [3]**
---The complex numbers $z$ and $w$ are given by
$$z = 8 + 3\text{i}, \quad w = -2\text{i}$$
Express in the form $a + b\text{i}$, where $a$ and $b$ are real constants,
\begin{enumerate}[label=(\alph*)]
\item $z - w$, [1]
\item $zw$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 2013 Q1 [3]}}