| Exam Board | Edexcel |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2011 |
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| Session | June |
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| Topic | Complex Numbers Arithmetic |
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| Type | Linear equations in z and z* |
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6. Given that \(z = x + \mathrm { i } y\), find the value of \(x\) and the value of \(y\) such that
$$z + 3 \mathrm { i } z ^ { * } = - 1 + 13 \mathrm { i }$$
where \(z ^ { * }\) is the complex conjugate of \(z\).