2013 A-level H2 Mathematics (9740) Paper 1 Question 8 Suggested Solutions

By KS Teng

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)
Since |z|=r, ~arg(z)=\theta

|w|=|(1-i\sqrt{3} )(z)|=(2)(r)=2r

arg(w)=arg[(1-i\sqrt{3} )(z)]=arg(1-i\sqrt{3} )+arg(z)=-\frac{\pi}{3}+\theta

(ii)

Graph of 8ii

Graph of 8ii

(iii)
arg(\frac{z^{10}}{w^{2}}) = 10 arg(z) - 2 arg(w) = \pi

10 \theta - 2 (\theta - \frac{\pi}{3}) = \pi

\theta = \frac{\pi}{24}

KS Comments:

This is a question that tests student on their understanding of the standard manipulation of modulus and argument. It is not difficult.

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