AQA Further AS Paper 1 2022 June — Question 4

Exam BoardAQA
ModuleFurther AS Paper 1 (Further AS Paper 1)
Year2022
SessionJune
TopicComplex Numbers Arithmetic
TypeMultiplication and powers of complex numbers

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}