| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2010 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Linear equations in z and z* |
| Difficulty | Moderate -0.3 This is a straightforward Further Maths FP1 question requiring students to substitute z = x + iy and z* = x - iy, then equate real and imaginary parts to solve a simple system of two linear equations. While it's a Further Maths topic, the algebraic manipulation is routine and mechanical with no conceptual challenges, making it slightly easier than average overall. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02e Arithmetic of complex numbers: add, subtract, multiply, divide |
3 The complex number $z$ satisfies the equation $z + 2 \mathrm { i } z ^ { * } = 12 + 9 \mathrm { i }$. Find $z$, giving your answer in the form $x + \mathrm { i } y$.
\hfill \mbox{\textit{OCR FP1 2010 Q3 [5]}}