AQA FP1 2009 June — Question 3

Exam BoardAQA
ModuleFP1 (Further Pure Mathematics 1)
Year2009
SessionJune
TopicComplex Numbers Arithmetic
TypeReal and imaginary part expressions
3 The complex number \(z\) is defined by $$z = x + 2 \mathrm { i }$$ where \(x\) is real.
  1. Find, in terms of \(x\), the real and imaginary parts of:
    1. \(z ^ { 2 }\);
    2. \(z ^ { 2 } + 2 z ^ { * }\).
  2. Show that there is exactly one value of \(x\) for which \(z ^ { 2 } + 2 z ^ { * }\) is real.
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