| Exam Board | OCR MEI |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2007 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Single locus sketching |
| Difficulty | Moderate -0.3 This is a straightforward Further Maths FP1 question testing standard complex number techniques: finding reciprocal by multiplying by conjugate, converting to modulus-argument form, and sketching basic loci (half-line and sector from a point). All parts are routine applications of well-practiced methods with no novel problem-solving required, though the Further Maths context places it slightly above typical A-level Core questions. |
| 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, divide4.02o Loci in Argand diagram: circles, half-lines |
It is given that $m = -4 + 2j$.
(i) Express $\frac{1}{m}$ in the form $a + bj$. [2]
(ii) Express $m$ in modulus-argument form. [4]
(iii) Represent the following loci on separate Argand diagrams.
(A) $\arg(z - m) = \frac{\pi}{4}$ [2]
(B) $0 \leq \arg(z - m) \leq \frac{\pi}{4}$ [3]8 It is given that $m = - 4 + 2 \mathrm { j }$.
\begin{enumerate}[label=(\roman*)]
\item Express $\frac { 1 } { m }$ in the form $a + b \mathrm { j }$.
\item Express $m$ in modulus-argument form.
\item Represent the following loci on separate Argand diagrams.\\
(A) $\arg ( z - m ) = \frac { \pi } { 4 }$\\
(B) $0 < \arg ( z - m ) < \frac { \pi } { 4 }$
\end{enumerate}
\hfill \mbox{\textit{OCR MEI FP1 2007 Q8 [11]}}