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If z is a complex number satisfying z + 1/z = 1, calculate z^2 + 1/z^2.
 

\(\phantom{z^10 + 1/z^10}\)

 

\(\phantom{z^3 + 1/z^3}\)

 Jun 27, 2022
 #1
avatar+124676 
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Square both sides

 

(z + 1/z) ^2 = 1^2

 

z^2 + 2 (z) (1/z)  +  1/z^2   =   1

 

z^2 +  2  + 1/z^2  =  1

 

z^2 + 1/z^2  =  1   -  2

 

z^2 + 1/z^2  =    -1

 

 

cool cool cool

 Jun 27, 2022

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