OCR FP1 2016 June — Question 2

Exam BoardOCR
ModuleFP1 (Further Pure Mathematics 1)
Year2016
SessionJune
TopicComplex Numbers Arithmetic
TypeModulus-argument form conversions

2 The complex number \(z\) has modulus \(2 \sqrt { 3 }\) and argument \(- \frac { 1 } { 3 } \pi\). Giving your answers in the form \(x + \mathrm { i } y\), where \(x\) and \(y\) are exact real numbers, and showing clearly how you obtain them, find
  1. \(z\),
  2. \(\frac { 1 } { \left( z ^ { * } - 5 \mathrm { i } \right) ^ { 2 } }\).