Edexcel FP2 2012 June — Question 3 8 marks

Exam BoardEdexcel
ModuleFP2 (Further Pure Mathematics 2)
Year2012
SessionJune
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicComplex numbers 2
TypeDirect nth roots: general complex RHS
DifficultyStandard +0.3 This is a standard FP2 question on converting to modulus-argument form and finding fourth roots using De Moivre's theorem. While it requires multiple steps (finding r and θ, then applying the formula for nth roots four times), these are routine procedures taught explicitly in the syllabus with no novel problem-solving required. The arithmetic is slightly elevated by the √3 term, but the method is completely algorithmic.
Spec4.02b Express complex numbers: cartesian and modulus-argument forms4.02r nth roots: of complex numbers

3. (a) Express the complex number \(- 2 + ( 2 \sqrt { 3 } ) \mathrm { i }\) in the form \(r ( \cos \theta + \mathrm { i } \sin \theta ) , - \pi < \theta \leqslant \pi\).
(b) Solve the equation $$z ^ { 4 } = - 2 + ( 2 \sqrt { } 3 ) i$$ giving the roots in the form \(r ( \cos \theta + \mathrm { i } \sin \theta ) , - \pi < \theta \leqslant \pi\).

3. (a) Express the complex number $- 2 + ( 2 \sqrt { 3 } ) \mathrm { i }$ in the form $r ( \cos \theta + \mathrm { i } \sin \theta ) , - \pi < \theta \leqslant \pi$.\\
(b) Solve the equation

$$z ^ { 4 } = - 2 + ( 2 \sqrt { } 3 ) i$$

giving the roots in the form $r ( \cos \theta + \mathrm { i } \sin \theta ) , - \pi < \theta \leqslant \pi$.\\

\hfill \mbox{\textit{Edexcel FP2 2012 Q3 [8]}}