2018 ACJC CA2 Q2
Timothy Gan
2018 ACJC CA2 Q2
Given that ${{\left( \frac{{{\left( 2-2\mathbf{i} \right)}^{2}}}{-\sqrt{3}+k\mathbf{i}} \right)}^{*}}=4{{\text{e}}^{\mathbf{i}\theta }}$, where $k$ is a positive real number and $-\pi <\theta \le \pi $,
(i)
Show that $k=1$,
[2]
(ii)
Hence find the exact value of $\theta $.
[4]
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