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# FP2 Complex numbers watch

1. z^5=4-4i
a) Solve this equation, giving your solutions in the form re^iϴ
b) Display these solutions on an argand diagram
c) Deduce that lpl=2sin(π/5) where p=e^(3πi/4)-e^(7πi/20)

Now I've done part a) and b) and I know I'm correct on those questions. In case you're wodering my solutions to a were:
z=√2e^(-πi/20)
z=√2e^(7πi/20)
z=√2e^(-9πi/20)
z=√2e^(3πi/4)
z=√2e^(-17πi/20)

I know that part c) is definetely related to part a), but I haven't got the slightest clue how to solve it algebraically. Could anyone please give me a hand and point me in the right direction?
2. okay I've worked it out. In terms of clues, use your answer to (b) to solve it geometrically. Just shout if you want a pic of my workings
3. (Original post by Darth_Narwhale)
okay I've worked it out. In terms of clues, use your answer to (b) to solve it geometrically. Just shout if you want a pic of my workings
Just solved it now. Didn't realise I had to use C3 knowledge what with double angle formulae and such. Thanks anyway!

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