These Ten-Year-Series (TYS) worked solutions with video explanations for 2013 A Level H2 Mathematics Paper 1 Question 8 are suggested by Mr Gan. For any comments or suggestions please contact us at support@timganmath.edu.sg.
2013 A Level H2 Math Paper 1 Question 8
The complex number $z$ is given by $z=r{{e}^{\text{i}\theta }}$, where $r>0$ and $0\le \theta \le \frac{1}{2}\pi $.
(i)
Given that $w=\left( 1-\text{i}\sqrt{3} \right)z$, find $\left| w \right|$ in terms of $r$ and $\arg w$ in terms of $\theta $.
[2]
(i) Given that $w=\left( 1-\text{i}\sqrt{3} \right)z$, find $\left| w \right|$ in terms of $r$ and $\arg w$ in terms of $\theta $.
[2]
(iii)
Given that $\arg \left( \frac{{{z}^{10}}}{{{w}^{2}}} \right)=\pi $, find $\theta $.
[3]
(ii) Given that $\arg \left( \frac{{{z}^{10}}}{{{w}^{2}}} \right)=\pi $, find $\theta $.
[3]
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