AQA FP1 2007 June — Question 3

Exam BoardAQA
ModuleFP1 (Further Pure Mathematics 1)
Year2007
SessionJune
TopicComplex Numbers Arithmetic
TypeLinear equations in z and z*

3 It is given that \(z = x + \mathrm { i } y\), where \(x\) and \(y\) are real numbers.
  1. Find, in terms of \(x\) and \(y\), the real and imaginary parts of $$z - 3 \mathbf { i } z ^ { * }$$ where \(z ^ { * }\) is the complex conjugate of \(z\).
  2. Find the complex number \(z\) such that $$z - 3 \mathrm { i } z ^ { * } = 16$$