OCR FP3 2007 January — Question 3

Exam BoardOCR
ModuleFP3 (Further Pure Mathematics 3)
Year2007
SessionJanuary
TopicComplex numbers 2

3
  1. Solve the equation \(z ^ { 2 } - 6 z + 36 = 0\), and give your answers in the form \(r ( \cos \theta \pm \mathrm { i } \sin \theta )\), where \(r > 0\) and \(0 \leqslant \theta \leqslant \pi\).
  2. Given that \(Z\) is either of the roots found in part (i), deduce the exact value of \(Z ^ { - 3 }\).