| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2021 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Complex arithmetic operations |
| Difficulty | Moderate -0.3 This is a straightforward multi-part question testing basic complex number operations. Part (a) uses Pythagoras to find λ, part (b) applies standard argument formula, part (c) requires routine algebraic manipulation (multiplying by conjugate and expanding), and part (d) is plotting points. All techniques are standard textbook exercises with no novel insight required, making it slightly easier than average. |
| 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 |
6. The complex number $z$ is defined by
$$z = - \lambda + 3 i \quad \text { where } \lambda \text { is a positive real constant }$$
Given that the modulus of $z$ is 5
\begin{enumerate}[label=(\alph*)]
\item write down the value of $\lambda$
\item determine the argument of $z$, giving your answer in radians to one decimal place.
In part (c) you must show detailed reasoning.\\
Solutions relying on calculator technology are not acceptable.
\item Express in the form $a + \mathrm { i } b$ where $a$ and $b$ are real,
\begin{enumerate}[label=(\roman*)]
\item $\frac { z + 3 i } { 2 - 4 i }$
\item $\mathrm { Z } ^ { 2 }$
\end{enumerate}\item Show on a single Argand diagram the points $A$, $B$, $C$ and $D$ that represent the complex numbers
$$z , z ^ { * } , \frac { z + 3 i } { 2 - 4 i } \text { and } z ^ { 2 }$$
\begin{center}
\end{center}
\begin{center}
\end{center}
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2021 Q6 [11]}}