2018 JJC P1 Q9 (b)
2018 JJC P1 Q9 (b)
5 marks
Prelims
The complex number \(w\) has modulus \(r\) and argument \(\theta \), where \(0<\theta <\frac{\pi }{2}\), and \(w^*\) denotes the conjugate of \(w\). State the modulus and argument of \(p\), where \(p=\frac{w}{w^*}\) .[2]
Given that \({{p}^{6}}\) is real and positive, find the possible values of \(\theta \).[3]
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Answer:\(|p| = 1\), \(\arg p = 2\theta\); \(\theta = \displaystyle\frac{\pi}{6}\) or \(\displaystyle\frac{\pi}{3}\)
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