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.

2 questions · Standard +0.0

4.02a Complex numbers: real/imaginary parts, modulus, argument4.02b Express complex numbers: cartesian and modulus-argument forms4.02c Complex notation: z, z*, Re(z), Im(z), |z|, arg(z)
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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 \(- \pi < \arg z < \pi\)
Pre-U Pre-U 9794/2 Specimen Q4
6 marks Standard +0.3
4 The complex number \(p\) satisfies the equation $$p + \mathrm { i } p ^ { * } = 2 \left( p - \mathrm { i } p ^ { * } \right) - 8$$ Determine the exact values of the modulus and argument of \(p\).