| Exam Board | OCR MEI |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2012 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Modulus and argument with operations |
| Difficulty | Standard +0.3 This is a straightforward Further Pure 1 question testing basic complex number conversions and geometric interpretation. Part (i) requires routine calculation of modulus and argument from Cartesian form, (ii) is direct conversion from polar to Cartesian form, and (iii) asks students to recognize that equal arguments mean collinearity—a standard observation. While FP1 content is inherently more advanced than Core modules, this particular question involves only mechanical calculations and simple geometric reasoning with no problem-solving insight required, making it slightly easier than average overall. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02b Express complex numbers: cartesian and modulus-argument forms4.02f Convert between forms: cartesian and modulus-argument4.02k Argand diagrams: geometric interpretation |
2 You are given that $z _ { 1 }$ and $z _ { 2 }$ are complex numbers.\\
$z _ { 1 } = 3 + 3 \sqrt { 3 } \mathrm { j }$, and $z _ { 2 }$ has modulus 5 and argument $\frac { \pi } { 3 }$.\\
(i) Find the modulus and argument of $z _ { 1 }$, giving your answers exactly.\\
(ii) Express $z _ { 2 }$ in the form $a + b \mathrm { j }$, where $a$ and $b$ are to be given exactly.\\
(iii) Explain why, when plotted on an Argand diagram, $z _ { 1 } , z _ { 2 }$ and the origin lie on a straight line.
\hfill \mbox{\textit{OCR MEI FP1 2012 Q2 [7]}}