OCR MEI FP1 2014 June — Question 8

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2014
SessionJune
TopicComplex Numbers Argand & Loci

8 You are given the complex number \(w = 2 + 2 \sqrt { 3 } \mathrm { j }\).
  1. Express \(w\) in modulus-argument form.
  2. Indicate on an Argand diagram the set of points, \(z\), which satisfy both of the following inequalities. $$- \frac { \pi } { 2 } \leqslant \arg z \leqslant \frac { \pi } { 3 } \text { and } | z | \leqslant 4$$ Mark \(w\) on your Argand diagram and find the greatest value of \(| z - w |\).