Complex conjugate properties

A question is this type if and only if it involves solving equations or manipulating expressions using complex conjugates, including equations like z + αz* = β.

1 questions · Moderate -0.3

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Edexcel F1 2018 June Q9
8 marks Moderate -0.3
9. Given that $$\frac { z - k \mathrm { i } } { z + 3 \mathrm { i } } = \mathrm { i } \text {, where } k \text { is a positive real constant }$$
  1. show that \(z = - \frac { ( k + 3 ) } { 2 } + \frac { ( k - 3 ) } { 2 } \mathrm { i }\)
  2. Using the printed answer in part (a),
    1. find an exact simplified value for the modulus of \(z\) when \(k = 4\)
    2. find the argument of \(z\) when \(k = 1\). Give your answer in radians to 3 decimal places, where \(- \pi < \arg z < \pi\)