| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Division plus modulus/argument |
| Difficulty | Moderate -0.3 This is a straightforward Further Maths question testing basic complex number operations: (a) requires algebraic manipulation to find w by multiplying both sides by w and rationalizing, (b) is a direct application of the arctan formula for argument. Both parts are routine calculations with no conceptual challenges, though being FP1 content places it slightly above average C3 difficulty. |
| 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, divide |
Given that $z = 22 + 4i$ and $\frac{z}{w} = 6 - 8i$, find
\begin{enumerate}[label=(\alph*)]
\item $w$ in the form $a + bi$, where $a$ and $b$ are real, [3]
\item the argument of $z$, in radians to 2 decimal places. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 Q1 [5]}}