Edexcel CP1 2022 June — Question 7

Exam BoardEdexcel
ModuleCP1 (Core Pure 1)
Year2022
SessionJune
TopicComplex Numbers Arithmetic
TypeEquations with z/z* or zz* terms
  1. Given that \(z = a + b \mathrm { i }\) is a complex number where \(a\) and \(b\) are real constants,
    1. show that \(z z ^ { * }\) is a real number.
    Given that
    • \(z z ^ { * } = 18\)
    • \(\frac { z } { z ^ { * } } = \frac { 7 } { 9 } + \frac { 4 \sqrt { 2 } } { 9 } \mathrm { i }\)
    • determine the possible complex numbers \(z\)
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