1. ## 2002 HSC help

Hi, this is Question 7 b from the 2002 HSC. I could do parts (i) - (iii) pretty easily but I'm struggling with (iv). I understand the solution up until it says "so OP3 = |z4| = 1". How do they know that OP3 = 1?? Also, can the exterior angle sum of a polygon be 4pi, 6pi, etc and not just 2pi?
Question: Screen Shot 2017-08-07 at 5.47.32 pm.png
Solution: Screen Shot 2017-08-07 at 5.47.53 pm.png

2. ## Re: 2002 HSC help

Hi,
According to the question pre-amble.
You are given in CIS form, $z_4$ $z_4 = \cos{(\alpha + 4 \beta)} + i \sin{(\alpha + 4 \beta)}$.
This means that $|z_4|=1$
Given that $z_4 = -OP_3 \Rightarrow |z_4|=|OP_3| \Rightarrow |OP_3|=1$.

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