| Exam Board | AQA |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2014 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Quadratic equations involving z² and z* |
| Difficulty | Standard +0.3 This is a straightforward complex number problem requiring substitution of z = a + bi, application of the conjugate definition, separation into real and imaginary parts, and solving two simultaneous linear equations. While it's a Further Maths topic, the technique is mechanical and standard for FP1, making it slightly easier than an average A-level question overall but typical for its module. |
| Spec | 4.02e Arithmetic of complex numbers: add, subtract, multiply, divide |
Find the complex number $z$ such that
$$5iz + 3z^* + 16 = 8i$$
Give your answer in the form $a + bi$, where $a$ and $b$ are real.
[6 marks]
\hfill \mbox{\textit{AQA FP1 2014 Q4 [6]}}