OCR MEI
Further Pure Core AS
2021
November
— Question 7
Exam Board
OCR MEI
Module
Further Pure Core AS (Further Pure Core AS)
Year
2021
Session
November
Topic
Complex Numbers Argand & Loci
7
Find the modulus and argument of \(z _ { 1 }\), where \(z _ { 1 } = 1 + \mathrm { i }\).
Given that \(\left| z _ { 2 } \right| = 2\) and \(\arg \left( z _ { 2 } \right) = \frac { 1 } { 6 } \pi\), express \(z _ { 2 }\) in a + bi form, where \(a\) and \(b\) are exact real numbers.
Using these results, find the exact value of \(\sin \frac { 5 } { 12 } \pi\), giving the answer in the form \(\frac { \sqrt { m } + \sqrt { n } } { p }\), where \(m , n\) and \(p\) are integers.