2023 ACJC P1 Q2
2023 ACJC P1 Q2
4 marks
Promo
Do not use a calculator in answering this question.
The complex numbers \(z\) and \(w\) satisfy the following equations.
\(w+{{z}^{*}}=-2+4\mathbf{i}\)
\(z+2=3\mathbf{i}w\)
Find \(z\) and \(w\) giving your answers in the form \(a+\mathbf{i}\,b\), where \(a\) and \(b\) are real numbers.[4]
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Answer:\(z=-\dfrac12-\dfrac92\mathrm{i}\), \(w=-\dfrac32-\dfrac12\mathrm{i}\)
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