| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2022 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Argand & Loci |
| Type | Complex arithmetic operations |
| Difficulty | Moderate -0.8 This is a straightforward Further Maths question testing basic complex number properties: using |z₁z₂| = |z₁||z₂| to find |z₂|, then applying the modulus formula with a given real part to find imaginary parts, and plotting on an Argand diagram. All steps are routine applications of standard formulas with no problem-solving insight required. |
| 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)4.02k Argand diagrams: geometric interpretation |
1.
$$z _ { 1 } = 3 + 3 i \quad z _ { 2 } = p + q i \quad p , q \in \mathbb { R }$$
Given that $\left| z _ { 1 } z _ { 2 } \right| = 15 \sqrt { 2 }$
\begin{enumerate}[label=(\alph*)]
\item determine $\left| z _ { 2 } \right|$
Given also that $p = - 4$
\item determine the possible values of $q$
\item Show $z _ { 1 }$ and the possible positions for $z _ { 2 }$ on the same Argand diagram.
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2022 Q1 [6]}}