Complex numbers, where do I even start?!

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AdamRuby
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#1
Report Thread starter 8 years ago
#1
Found these questions on a uni past paper and I don't even know where to start, any guidance?

I managed to get part a down (so being full of confidence had a go at part b, now I'm regretting it) so I can tell you part a has nothing to do with b/c

(hopefully the attachment works!)

thanks!
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WhiteGroupMaths
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#2
Report 8 years ago
#2
Let me give you a little assistance for (b) :

to solve z^4 = -16, rewrite -16 as 16*(-1)= 16*e^i(π + 2kπ) , where k=0 ,1 ,2 and 3

Thereafter, If you quad root both sides,

you would arrive at

z = 2 *e^i [(π + 2kπ)/4]

You should be able to obtain the roots of the equation from this point onwards.

Hope it helps. Peace.
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DFranklin
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#3
Report 8 years ago
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For (c) note 16 \cos^4 \theta = (e^{i\theta}+e^{-i\theta})^4; expand RHS using the binomial theorem, then note 2 \cos 2\theta = e^{2i\theta} + e^{-2i\theta} etc.
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