OCR Further Pure Core AS Specimen — Question 2

Exam BoardOCR
ModuleFurther Pure Core AS (Further Pure Core AS)
SessionSpecimen
TopicComplex Numbers Arithmetic
TypeMultiplication and powers of complex numbers

2 In this question you must show detailed reasoning.
Given that \(z _ { 1 } = 3 + 2 \mathrm { i }\) and \(z _ { 2 } = - 1 - \mathrm { i }\), find the following, giving each in the form \(a + b \mathrm { i }\).
  1. \(z _ { 1 } ^ { * } z _ { 2 }\)
  2. \(\frac { z _ { 1 } + 2 z _ { 2 } } { z _ { 2 } }\)