AQA Further AS Paper 1 2022 June — Question 4 1 marks

Exam BoardAQA
ModuleFurther AS Paper 1 (Further AS Paper 1)
Year2022
SessionJune
Marks1
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicComplex Numbers Arithmetic
TypeMultiplication and powers of complex numbers
DifficultyEasy -1.2 This is a straightforward multiple-choice question testing direct recall of the multiplication rule for complex numbers in modulus-argument form: multiply moduli (2×3=6) and add arguments (α+β). No calculation or problem-solving required beyond recognizing the standard formula.
Spec4.02b Express complex numbers: cartesian and modulus-argument forms4.02e Arithmetic of complex numbers: add, subtract, multiply, divide
4 The complex numbers \(w\) and \(z\) are defined as $$\begin{aligned} w & = 2 ( \cos \alpha + \mathrm { i } \sin \alpha ) \\ z & = 3 ( \cos \beta + \mathrm { i } \sin \beta ) \end{aligned}$$ Find the product \(w z\) Tick \(( \checkmark )\) one box. $$\begin{aligned} & 5 ( \cos ( \alpha \beta ) + \mathrm { i } \sin ( \alpha \beta ) ) \\ & 6 ( \cos ( \alpha \beta ) + \mathrm { i } \sin ( \alpha \beta ) ) \\ & 5 ( \cos ( \alpha + \beta ) + \mathrm { i } \sin ( \alpha + \beta ) ) \\ & 6 ( \cos ( \alpha + \beta ) + \mathrm { i } \sin ( \alpha + \beta ) ) \end{aligned}$$ \includegraphics[max width=\textwidth, alt={}, center]{fd9715c4-9ce1-4608-aed6-f3d4f71208b5-03_113_113_762_1206} \includegraphics[max width=\textwidth, alt={}, center]{fd9715c4-9ce1-4608-aed6-f3d4f71208b5-03_108_108_900_1206} \includegraphics[max width=\textwidth, alt={}, center]{fd9715c4-9ce1-4608-aed6-f3d4f71208b5-03_113_113_1032_1206}
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Question 4:
AnswerMarks Guidance
AnswerMarks Guidance
\(6(\cos(\alpha+\beta) + i\sin(\alpha+\beta))\)B1 (AO1.1b) Ticks the correct box 
**Question 4:**

| Answer | Marks | Guidance |
|--------|-------|----------|
| $6(\cos(\alpha+\beta) + i\sin(\alpha+\beta))$ | B1 (AO1.1b) | Ticks the correct box |
4 The complex numbers $w$ and $z$ are defined as

$$\begin{aligned}
w & = 2 ( \cos \alpha + \mathrm { i } \sin \alpha ) \\
z & = 3 ( \cos \beta + \mathrm { i } \sin \beta )
\end{aligned}$$

Find the product $w z$\\
Tick $( \checkmark )$ one box.

$$\begin{aligned}
& 5 ( \cos ( \alpha \beta ) + \mathrm { i } \sin ( \alpha \beta ) ) \\
& 6 ( \cos ( \alpha \beta ) + \mathrm { i } \sin ( \alpha \beta ) ) \\
& 5 ( \cos ( \alpha + \beta ) + \mathrm { i } \sin ( \alpha + \beta ) ) \\
& 6 ( \cos ( \alpha + \beta ) + \mathrm { i } \sin ( \alpha + \beta ) )
\end{aligned}$$

\includegraphics[max width=\textwidth, alt={}, center]{fd9715c4-9ce1-4608-aed6-f3d4f71208b5-03_113_113_762_1206}\\
\includegraphics[max width=\textwidth, alt={}, center]{fd9715c4-9ce1-4608-aed6-f3d4f71208b5-03_108_108_900_1206}\\
\includegraphics[max width=\textwidth, alt={}, center]{fd9715c4-9ce1-4608-aed6-f3d4f71208b5-03_113_113_1032_1206}\\
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\hfill \mbox{\textit{AQA Further AS Paper 1 2022 Q4 [1]}}
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Q1 1 Q2 1 Q3 1 Q4 1 Q5 3 Q6 5 Q7 9 Q8 7 Q9 5 Q10 6 Q11 4 Q12 6 Q13 10 Q14 15 Q15 6