De moivre's theorem complex number

kelvin macks
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can anyone explain how ro make the working above the red circle to the working in the red circle? why the author do this?
 

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It's equivalent to having

(a+b)c = ac+bc

where

a=z^2+\frac{1}{z^2}

b=2

c=z^2-\frac{1}{z^2}

and why he did it should be pretty evident from his next two lines.
 
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It has nothing to do with "complex numbers" or "DeMoivre's Theorem". It is, as mentallic said, just the distributive law.
 
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Hahaha, this is something Feynman talked about from his childhood. What you've presented is actually a higher-order form of something called Morrie's[/PLAIN] Law (Feynman's little friend in childhood). From what I've studied, a useful application is in the proof of http://2000clicks.com/MathHelp/GeometryTriangleUrquhartsTheorem.aspx.
 
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