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complex number stuffs (1 Viewer)

synthesisFR

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could someone please help show me how to do these ( the ones in yellow) in a logical way? thank you so much!
i was trying doing them in my maths class today given as revision questions but couldnt figure them out...
 

SadCeliac

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surely for 13c you can do difference of two squares over and over?? wait let me try
 

synthesisFR

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Could you even just sub in z = [cis(theta)]^2 ???
the solution he wrote was subbing in z = (cos2(theta)-1)/2


but it makes more sense to sub in sin^2theta instead

ik its the same but like skipping that one step confsued me so much rip
 

tywebb

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These are Cambridge Ext 2 Ex 3C Q13-15

Here the solutions to 13b,c,14c,15a. I included 13b too because the solution to 13c refers to part of the solution to 13b .

13b.png

13c.png
14c.png
15a-1.png
15a-2.png
 
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tywebb

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There is yet a third even quicker way using the hyperbolic cotangent method, which is outside the syllabus, but actually much easier:





 
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