| Exam Board | OCR MEI |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2011 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Modulus-argument form conversions |
| Difficulty | Moderate -0.8 This is a straightforward Further Maths FP1 question testing basic complex number operations: addition, division (requiring conjugate multiplication), and conversion to modulus-argument form. All parts are routine calculations with standard techniques and no problem-solving insight required. While FP1 content, these are foundational skills practiced extensively, making it easier than average overall. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02b Express complex numbers: cartesian and modulus-argument forms4.02e Arithmetic of complex numbers: add, subtract, multiply, divide4.02f Convert between forms: cartesian and modulus-argument4.02k Argand diagrams: geometric interpretation |
2 You are given that $z = 3 - 2 \mathrm { j }$ and $w = - 4 + \mathrm { j }$.\\
(i) Express $\frac { z + w } { w }$ in the form $a + b \mathrm { j }$.\\
(ii) Express $w$ in modulus-argument form.\\
(iii) Show $w$ on an Argand diagram, indicating its modulus and argument.
\hfill \mbox{\textit{OCR MEI FP1 2011 Q2 [8]}}