AQA FP1 2012 January — Question 3

Exam BoardAQA
ModuleFP1 (Further Pure Mathematics 1)
Year2012
SessionJanuary
TopicComplex Numbers Arithmetic
TypeMultiplication and powers of complex numbers
3
  1. Solve the following equations, giving each root in the form \(a + b \mathrm { i }\) :
    1. \(x ^ { 2 } + 9 = 0\);
    2. \(( x + 2 ) ^ { 2 } + 9 = 0\).
    1. Expand \(( 1 + x ) ^ { 3 }\).
    2. Express \(( 1 + 2 \mathrm { i } ) ^ { 3 }\) in the form \(a + b \mathrm { i }\).
    3. Given that \(z = 1 + 2 \mathrm { i }\), find the value of $$z ^ { * } - z ^ { 3 }$$
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