OCR MEI Further Pure Core 2021 November — Question 3

Exam BoardOCR MEI
ModuleFurther Pure Core (Further Pure Core)
Year2021
SessionNovember
TopicComplex Numbers Argand & Loci

3 In this question you must show detailed reasoning.
The complex numbers \(z _ { 1 }\) and \(z _ { 2 }\) are given by \(z _ { 1 } = - 2 + 2 i\) and \(z _ { 2 } = 2 \left( \cos \frac { 1 } { 6 } \pi + i \sin \frac { 1 } { 6 } \pi \right)\).
  1. Find the modulus and argument of \(z _ { 1 }\).
  2. Hence express \(\frac { z _ { 1 } } { z _ { 2 } }\) in exact modulus-argument form.