| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2015 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Complex arithmetic operations |
| Difficulty | Moderate -0.3 This is a straightforward Further Maths question testing standard complex number operations: finding modulus/argument, complex division, squaring, conjugate, and plotting. All parts use routine techniques with no novel problem-solving required, though it's slightly above average difficulty due to being Further Maths content. |
| 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, divide4.02k Argand diagrams: geometric interpretation |
7.
$$z = - 3 k - 2 k \mathrm { i } , \text { where } k \text { is a real, positive constant. }$$
\begin{enumerate}[label=(\alph*)]
\item Find the modulus and the argument of $z$, giving the argument in radians to 2 decimal places and giving the modulus as an exact answer in terms of $k$.
\item Express in the form $a + \mathrm { i } b$, where $a$ and $b$ are real and are given in terms of $k$ where necessary,
\begin{enumerate}[label=(\roman*)]
\item $\frac { 4 } { z + 3 k }$
\item $z ^ { 2 }$
\end{enumerate}\item Given that $k = 1$, plot the points $A , B , C$ and $D$ representing $z , z ^ { * } , \frac { 4 } { z + 3 k }$ and $z ^ { 2 }$ respectively on a single Argand diagram.
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2015 Q7 [11]}}