Edexcel FP1 2013 June — Question 3

Exam BoardEdexcel
ModuleFP1 (Further Pure Mathematics 1)
Year2013
SessionJune
TopicComplex Numbers Argand & Loci

3. $$z _ { 1 } = \frac { 1 } { 2 } ( 1 + \mathrm { i } \sqrt { } 3 ) , z _ { 2 } = - \sqrt { } 3 + \mathrm { i }$$
  1. Express \(z _ { 1 }\) and \(z _ { 2 }\) in the form \(r ( \cos \theta + \mathrm { i } \sin \theta )\) giving exact values of \(r\) and \(\theta\).
    (4)
  2. Find \(\left| z _ { 1 } z _ { 2 } \right|\).
  3. Show and label \(z _ { 1 }\) and \(z _ { 2 }\) on a single Argand diagram.
    (2)