AQA FP1 2013 January — Question 2

Exam BoardAQA
ModuleFP1 (Further Pure Mathematics 1)
Year2013
SessionJanuary
TopicComplex Numbers Arithmetic
TypeMulti-part questions with division as one step
2
  1. Solve the equation \(w ^ { 2 } + 6 w + 34 = 0\), giving your answers in the form \(p + q \mathrm { i }\), where \(p\) and \(q\) are integers.
  2. It is given that \(z = \mathrm { i } ( 1 + \mathrm { i } ) ( 2 + \mathrm { i } )\).
    1. Express \(z\) in the form \(a + b \mathrm { i }\), where \(a\) and \(b\) are integers.
    2. Find integers \(m\) and \(n\) such that \(z + m z ^ { * } = n \mathrm { i }\).
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