| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2018 |
| Session | Specimen |
| 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 students to simplify a complex fraction (by multiplying by conjugate), then solve a linear system using z = a + bi and z* = a - bi. While it involves multiple steps (fraction simplification, substituting z and z*, solving simultaneous equations), each step is routine and the method is standard textbook material. Slightly easier than average due to its mechanical nature, though the Further Maths context places it at a reasonable baseline. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02e Arithmetic of complex numbers: add, subtract, multiply, divide |
5.
$$2 z + z ^ { * } = \frac { 3 + 4 \mathrm { i } } { 7 + \mathrm { i } }$$
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 2018 Q5 [5]}}