| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2016 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Linear equations in z and z* |
| Difficulty | Moderate -0.3 This is a straightforward Further Maths question requiring simplification of a complex fraction (by multiplying by conjugate) and solving a linear system using z = x + iy and z* = x - iy. While it involves multiple steps, each is routine: simplify RHS, substitute z and z*, solve simultaneous equations. The techniques are standard for F1 complex numbers with no conceptual difficulty or novel insight required. |
| Spec | 4.02e Arithmetic of complex numbers: add, subtract, multiply, divide |
5.
$$2 z + z ^ { * } = \frac { 3 + 4 i } { 7 + i }$$
Find $z$, giving your answer in the form $a + b \mathrm { i }$, where $a$ and $b$ are real constants. You must show all your working.\\
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\hfill \mbox{\textit{Edexcel F1 2016 Q5 [5]}}