AQA FP1 2011 June — Question 3

Exam BoardAQA
ModuleFP1 (Further Pure Mathematics 1)
Year2011
SessionJune
TopicComplex Numbers Arithmetic
TypeEquations with z/z* or zz* terms

3 It is given that \(z = x + \mathrm { i } y\), where \(x\) and \(y\) are real.
  1. Find, in terms of \(x\) and \(y\), the real and imaginary parts of $$( z - \mathrm { i } ) \left( z ^ { * } - \mathrm { i } \right)$$
  2. Given that $$( z - \mathrm { i } ) \left( z ^ { * } - \mathrm { i } \right) = 24 - 8 \mathrm { i }$$ find the two possible values of \(z\).