| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2017 |
| Session | June |
| Marks | 10 |
| 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 (routine formulas), algebraic manipulation to find w, and plotting on an Argand diagram. All parts are mechanical applications of basic complex number techniques with no novel insight required, making it slightly easier than average even for Further Maths. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02b Express complex numbers: cartesian and modulus-argument forms4.02c 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 |
9.
$$z = \frac { 1 } { 5 } - \frac { 2 } { 5 } \mathrm { i }$$
\begin{enumerate}[label=(\alph*)]
\item Find the modulus and the argument of $z$, giving the modulus as an exact answer and giving the argument in radians to 2 decimal places.
Given that
$$\mathrm { zw } = \lambda \mathrm { i }$$
where $\lambda$ is a real constant,
\item find $w$ in the form $a + \mathrm { i } b$, where $a$ and $b$ are real. Give your answer in terms of $\lambda$.
\item Given that $\lambda = \frac { 1 } { 10 }$
\begin{enumerate}[label=(\roman*)]
\item find $\frac { 4 } { 3 } ( z + w )$,
\item plot the points $A , B , C$ and $D$, representing $z , z w , w$ and $\frac { 4 } { 3 } ( z + w )$ respectively, on a single Argand diagram.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2017 Q9 [10]}}