Edexcel FP1 2011 June — Question 2

Exam BoardEdexcel
ModuleFP1 (Further Pure Mathematics 1)
Year2011
SessionJune
TopicComplex Numbers Arithmetic
TypeStandard quadratic with real coefficients

2. $$z _ { 1 } = - 2 + \mathrm { i }$$
  1. Find the modulus of \(z _ { 1 }\).
  2. Find, in radians, the argument of \(z _ { 1 }\), giving your answer to 2 decimal places. The solutions to the quadratic equation $$z ^ { 2 } - 10 z + 28 = 0$$ are \(z _ { 2 }\) and \(z _ { 3 }\).
  3. Find \(z _ { 2 }\) and \(z _ { 3 }\), giving your answers in the form \(p \pm i \sqrt { } q\), where \(p\) and \(q\) are integers.
  4. Show, on an Argand diagram, the points representing your complex numbers \(z _ { 1 } , z _ { 2 }\) and \(z _ { 3 }\).