De moivre's theorem complex number

1. May 31, 2014

kelvin macks

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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2. May 31, 2014

Mentallic

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.

3. May 31, 2014

HallsofIvy

It has nothing to do with "complex numbers" or "DeMoivre's Theorem". It is, as mentallic said, just the distributive law.

4. May 31, 2014

harmonic_lens

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] [Broken] Law (Feynman's little friend in childhood). From what I've studied, a useful application is in the proof of Urquhart's Theorem.

Last edited by a moderator: May 6, 2017