| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2016 |
| Session | Specimen |
| Marks | 6 |
| Topic | Complex Numbers Arithmetic |
| Type | Division plus other arithmetic operations |
| Difficulty | Easy -1.3 This is a straightforward multi-part question testing basic complex number operations: conjugate addition, division by a complex number (requiring multiplication by conjugate), and plotting on an Argand diagram. All are routine procedures with no problem-solving required, making it easier than average. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02e Arithmetic of complex numbers: add, subtract, multiply, divide4.02k Argand diagrams: geometric interpretation |
**Question 9(i)**
- $z^* = 3 + 4\text{i}$ seen or implied — B1
- $9 - 4\text{i}$ obtained — B1
**Question 9(ii)**
- Multiply by conjugate — M1
- $\dfrac{3}{5} + \dfrac{4}{5}\text{i}$ or equivalent — A1
**Question 9(iii)**
- Show $3 - 4\text{i}$ on an Argand diagram — B1
- Show $3 + 4\text{i}$ on an Argand diagram — B1ft
**Total: 6 marks**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\\
(i) $2 z + z ^ { * }$,\\
(ii) $\frac { 5 } { z }$.\\
(iii) Show $z$ and $z ^ { * }$ on an Argand diagram.
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2016 Q9 [6]}}