Edexcel FP2 — Question 11 3 marks

Exam BoardEdexcel
ModuleFP2 (Further Pure Mathematics 2)
Marks3
PaperDownload PDF ↗
TopicComplex numbers 2
TypeComplex number arithmetic and simplification
DifficultyModerate -0.8 This is a straightforward application of the multiplication rule for complex numbers in polar form: multiply moduli and add arguments. The calculation is routine (r=12, θ=π/4+2π/3=11π/12) with no conceptual difficulty or problem-solving required, making it easier than average even for Further Maths.
Spec4.02e Arithmetic of complex numbers: add, subtract, multiply, divide
$$z = 4\left(\cos \frac{\pi}{4} + i\sin \frac{\pi}{4}\right) \text{ and } w = 3\left(\cos \frac{2\pi}{3} + i\sin \frac{2\pi}{3}\right).$$ Express \(zw\) in the form \(r(\cos \theta + i \sin \theta)\), \(r > 0\), \(-\pi < \theta < \pi\). [3] 
$$z = 4\left(\cos \frac{\pi}{4} + i\sin \frac{\pi}{4}\right) \text{ and } w = 3\left(\cos \frac{2\pi}{3} + i\sin \frac{2\pi}{3}\right).$$

Express $zw$ in the form $r(\cos \theta + i \sin \theta)$, $r > 0$, $-\pi < \theta < \pi$.
[3]

\hfill \mbox{\textit{Edexcel FP2  Q11 [3]}}
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