AQA FP2 2012 January — Question 5

Exam BoardAQA
ModuleFP2 (Further Pure Mathematics 2)
Year2012
SessionJanuary
TopicComplex numbers 2

5 Find the smallest positive integer values of \(p\) and \(q\) for which $$\frac { \left( \cos \frac { \pi } { 8 } + \mathrm { i } \sin \frac { \pi } { 8 } \right) ^ { p } } { \left( \cos \frac { \pi } { 12 } - \mathrm { i } \sin \frac { \pi } { 12 } \right) ^ { q } } = \mathrm { i }$$