Edexcel FP2 2003 June — Question 9 3 marks

Exam BoardEdexcel
ModuleFP2 (Further Pure Mathematics 2)
Year2003
SessionJune
Marks3
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Mark schemeDownload 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 requires only direct substitution (r₁r₂ = 12, θ₁+θ₂ = π/4 + 2π/3 = 11π/12) with no conceptual difficulty or problem-solving insight needed.
Spec4.02b Express complex numbers: cartesian and modulus-argument forms4.02e Arithmetic of complex numbers: add, subtract, multiply, divide
9. $$z = 4 \left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right) , \text { and } \boldsymbol { w } = 3 \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$$ Express zw in the form \(r ( \cos \theta + \mathrm { i } \sin \theta ) , r > 0 , - \pi < \theta < \pi\).
9.

$$z = 4 \left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right) , \text { and } \boldsymbol { w } = 3 \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$$

Express zw in the form $r ( \cos \theta + \mathrm { i } \sin \theta ) , r > 0 , - \pi < \theta < \pi$.\\

\hfill \mbox{\textit{Edexcel FP2 2003 Q9 [3]}}
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