Edexcel FP1 2012 January — Question 5

Exam BoardEdexcel
ModuleFP1 (Further Pure Mathematics 1)
Year2012
SessionJanuary
TopicComplex Numbers Arithmetic
TypeGiven one complex root, find all roots
5. The roots of the equation $$z ^ { 3 } - 8 z ^ { 2 } + 22 z - 20 = 0$$ are \(z _ { 1 } , z _ { 2 }\) and \(z _ { 3 }\).
  1. Given that \(z _ { 1 } = 3 + \mathrm { i }\), find \(z _ { 2 }\) and \(z _ { 3 }\).
  2. Show, on a single Argand diagram, the points representing \(z _ { 1 } , z _ { 2 }\) and \(z _ { 3 }\).
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