OCR MEI FP1 2011 June — Question 2 8 marks

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2011
SessionJune
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicComplex Numbers Arithmetic
TypeModulus-argument form conversions
DifficultyModerate -0.8 This is a straightforward Further Maths FP1 question testing basic complex number operations: addition, division (requiring conjugate multiplication), and conversion to modulus-argument form. All parts are routine calculations with standard techniques and no problem-solving insight required. While FP1 content, these are foundational skills practiced extensively, making it easier than average overall.
Spec4.02a Complex numbers: real/imaginary parts, modulus, argument4.02b Express complex numbers: cartesian and modulus-argument forms4.02e Arithmetic of complex numbers: add, subtract, multiply, divide4.02f Convert between forms: cartesian and modulus-argument4.02k Argand diagrams: geometric interpretation

2 You are given that \(z = 3 - 2 \mathrm { j }\) and \(w = - 4 + \mathrm { j }\).
  1. Express \(\frac { z + w } { w }\) in the form \(a + b \mathrm { j }\).
  2. Express \(w\) in modulus-argument form.
  3. Show \(w\) on an Argand diagram, indicating its modulus and argument.

2 You are given that $z = 3 - 2 \mathrm { j }$ and $w = - 4 + \mathrm { j }$.\\
(i) Express $\frac { z + w } { w }$ in the form $a + b \mathrm { j }$.\\
(ii) Express $w$ in modulus-argument form.\\
(iii) Show $w$ on an Argand diagram, indicating its modulus and argument.

\hfill \mbox{\textit{OCR MEI FP1 2011 Q2 [8]}}