| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Simultaneous equations with complex numbers |
| Difficulty | Standard +0.3 This is a straightforward simultaneous equations problem with complex numbers requiring basic algebraic manipulation (elimination/substitution) and a standard argument calculation. While it's Further Maths content, the techniques are routine and mechanical with no conceptual challenges, making it slightly easier than average overall. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02e Arithmetic of complex numbers: add, subtract, multiply, divide |
The complex numbers $z$ and $w$ satisfy the simultaneous equations
$$2z + iw = -1,$$
$$z - w = 3 + 3i.$$
\begin{enumerate}[label=(\alph*)]
\item Use algebra to find $z$, giving your answers in the form $a + ib$, where $a$ and $b$ are real. [4]
\item Calculate $\arg z$, giving your answer in radians to 2 decimal places. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 Q33 [6]}}