Random Questions from 2016 Prelims #6

HCI P1 Q5

Sketch on a single Argand diagram, the loci defined by -\frac{\pi}{4} \textless \text{arg}(z+1+2i) \le \frac{\pi}{4} and |(2+i)w+5| \le \sqrt{5}

(i) Find the minimum value of \text{arg}(w)

(ii) Find the minimum value of |z-w|

(iii) Given that \text{arg}(z-w) \textless \theta, - \pi \textless \theta \le \pi, state the minimum value of \theta

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