9709 P31 - Jun 2014 - Q5
1988
The complex number \(z\) is defined by \(z = \frac{9\sqrt{3} + 9i}{\sqrt{3} - i}\). Find, showing all your working,
(i) an expression for \(z\) in the form \(re^{i\theta}\), where \(r > 0\) and \(-\pi < \theta \leq \pi\),
(ii) the two square roots of \(z\), giving your answers in the form \(re^{i\theta}\), where \(r > 0\) and \(-\pi < \theta \leq \pi\).
