| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2009 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Complex arithmetic operations |
| Difficulty | Moderate -0.8 This is a straightforward FP1 question testing basic complex number operations: plotting points, finding modulus (using Pythagoras), finding argument (using arctan), and division (multiplying by conjugate). All are standard procedures with no problem-solving required, making it easier than average even for Further Maths. |
| Spec | 4.02c Complex notation: z, z*, Re(z), Im(z), |z|, arg(z)4.02e Arithmetic of complex numbers: add, subtract, multiply, divide4.02k Argand diagrams: geometric interpretation |
\begin{enumerate}
\item The complex numbers $z _ { 1 }$ and $z _ { 2 }$ are given by
\end{enumerate}
$$z _ { 1 } = 2 - i \quad \text { and } \quad z _ { 2 } = - 8 + 9 i$$
(a) Show $z _ { 1 }$ and $z _ { 2 }$ on a single Argand diagram.
Find, showing your working,\\
(b) the value of $\left| z _ { 1 } \right|$,\\
(c) the value of $\arg z _ { 1 }$, giving your answer in radians to 2 decimal places,\\
(d) $\frac { Z _ { 2 } } { Z _ { 1 } }$ in the form $a + b \mathrm { i }$, where $a$ and $b$ are real.\\
\hfill \mbox{\textit{Edexcel FP1 2009 Q1 [8]}}