SPS SPS FM Pure 2026 November — Question 1

Exam BoardSPS
ModuleSPS FM Pure (SPS FM Pure)
Year2026
SessionNovember
TopicComplex Numbers Arithmetic
TypeLinear equations in z and z*
  1. The complex number \(z\) satisfies the equation \(z + 2 \mathrm { i } z ^ { * } + 1 - 4 \mathrm { i } = 0\).
You are given that \(z = x + \mathrm { i } y\), where \(x\) and \(y\) are real numbers.
Determine the values of \(x\) and \(y\).
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