CAIE P3 2012 June — Question 4

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2012
SessionJune
TopicComplex Numbers Argand & Loci

4 The complex number \(u\) is defined by \(u = \frac { ( 1 + 2 \mathrm { i } ) ^ { 2 } } { 2 + \mathrm { i } }\).
  1. Without using a calculator and showing your working, express \(u\) in the form \(x + \mathrm { i } y\), where \(x\) and \(y\) are real.
  2. Sketch an Argand diagram showing the locus of the complex number \(z\) such that \(| z - u | = | u |\).