2013 PJC P1 Q10

2013 PJC P1 Q10

The complex number \(w\) has modulus \(3\) and argument \(\frac{3\pi }{4}\) and \(w^*\) denotes the conjugate of \(w\).
Find the modulus and argument of \(p\), where \(p=\frac{1-\mathbf{i}}{{{w}^{*}}}\).

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Answer:\(|p|=\dfrac{\sqrt2}{3}\), \(\arg(p)=\dfrac\pi2\)

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