2022 CJC J2 MYE P1 Q7
Timothy Gan
2022 CJC J2 MYE P1 Q7
(a)
The complex number $z$ is given by $z=r{{\text{e}}^{\text{i}\theta }}$ where $r>0$ and $-\frac{2\pi }{3}\le \theta \le \frac{2\pi }{3}$.
(i) Given that $w=\left( \frac{\sqrt{3}}{4}-\frac{1}{4}\text{i} \right)z$, find the modulus and argument of $w$, leaving your answers in terms of $r$ and $\theta $.
[3]
(ii) Find the possible values of $\theta $ if $w$ is purely imaginary.
[3]
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