AQA FP1 2010 January — Question 2

Exam BoardAQA
ModuleFP1 (Further Pure Mathematics 1)
Year2010
SessionJanuary
TopicComplex Numbers Arithmetic
TypeMultiplication and powers of complex numbers
2 The complex number \(z\) is defined by $$z = 1 + \mathrm { i }$$
  1. Find the value of \(z ^ { 2 }\), giving your answer in its simplest form.
  2. Hence show that \(z ^ { 8 } = 16\).
  3. Show that \(\left( z ^ { * } \right) ^ { 2 } = - z ^ { 2 }\).
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