OCR FP3 2007 June — Question 1

Exam BoardOCR
ModuleFP3 (Further Pure Mathematics 3)
Year2007
SessionJune
TopicComplex numbers 2
1
  1. By writing \(z\) in the form \(r \mathrm { e } ^ { \mathrm { i } \theta }\), show that \(z z ^ { * } = | z | ^ { 2 }\).
  2. Given that \(z z ^ { * } = 9\), describe the locus of \(z\).
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