<PRE><B>Question 704871</B>
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ z^4\ +\ z^2\ +\ 1]


The only thing you can add to something and not change the value of the original expression is zero.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ z^4\ +\ z^2\ +\ 1\ +\ 0]


But *[tex \LARGE z^2\ -\ z^2\ =\ 0], so replace the zero with *[tex \LARGE z^2\ -\ z^2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ z^4\ +\ z^2\ +\ 1\ +\ z^2\ -\ z^2]


Then collect like terms:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ z^4\ +\ 2z^2\ +\ 1\ -\ z^2]


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
&lt;font face=&quot;Math1&quot; size=&quot;+2&quot;&gt;Egw to Beta kai to Sigma&lt;/font&gt;
My calculator said it, I believe it, that settles it
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