AQA FP1 2007 January — Question 1

Exam BoardAQA
ModuleFP1 (Further Pure Mathematics 1)
Year2007
SessionJanuary
TopicComplex Numbers Arithmetic
TypeVerifying roots satisfy equations
1
  1. Solve the following equations, giving each root in the form \(a + b \mathrm { i }\) :
    1. \(x ^ { 2 } + 16 = 0\);
    2. \(x ^ { 2 } - 2 x + 17 = 0\).
    1. Expand \(( 1 + x ) ^ { 3 }\).
    2. Express \(( 1 + \mathrm { i } ) ^ { 3 }\) in the form \(a + b \mathrm { i }\).
    3. Hence, or otherwise, verify that \(x = 1 + \mathrm { i }\) satisfies the equation $$x ^ { 3 } + 2 x - 4 \mathrm { i } = 0$$
This paper (8 questions)
View full paper
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8