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If z is a complex number satisfying
z + 1/z = 1,

then compute z^2 + 1/z^2.

 May 9, 2022
 #1
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z^2 + 1/z^2 = -4.

 May 9, 2022
 #2
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\(z^2 + 2 + \dfrac1{z^2} = \left(z + \dfrac1z\right)^2 = 1\\ z^2 + \dfrac1{z^2} = 1 - 2 = -1\)

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 May 9, 2022

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