| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2020 |
| Session | Specimen |
| Marks | 2 |
| Topic | Complex Numbers Arithmetic |
| Type | Division plus other arithmetic operations |
| Difficulty | Easy -1.2 This is a straightforward complex numbers question testing basic operations: arithmetic with conjugates, division by a complex number (requiring multiplication by conjugate), and plotting on an Argand diagram. All three parts are routine procedures with no problem-solving required, making it easier than average but not trivial since it requires correct execution of standard techniques. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02e Arithmetic of complex numbers: add, subtract, multiply, divide4.02k Argand diagrams: geometric interpretation |
(a) $z^* = 3 + 4\text{i}$ seen or implied — **B1**
$9 - 4\text{i}$ obtained — **B1**
**Total: 2**
(b) Multiply by conjugate — **M1**
$\dfrac{3}{5} + \dfrac{4}{5}\text{i}$ or equivalent — **A1**
**Total: 2**
(c) Show $3 - 4\text{i}$ on an Argand diagram — **B1**
Show $3 + 4\text{i}$ on an Argand diagram — **B1** (B1ft)
**Total: 2**9 The complex number $3 - 4 \mathrm { i }$ is denoted by $z$. Giving your answers in the form $x + \mathrm { i } y$, and showing clearly how you obtain them, find
\begin{enumerate}[label=(\alph*)]
\item $2 z + z ^ { * }$,
\item $\frac { 5 } { z }$.
\item Show $z$ and $z ^ { * }$ on an Argand diagram.
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2020 Q9 [2]}}