If z is a complex number satisfying z + 1/z = 1,
then compute z^2 + 1/z^2.
z^2 + 1/z^2 = -4.
\(z^2 + 2 + \dfrac1{z^2} = \left(z + \dfrac1z\right)^2 = 1\\ z^2 + \dfrac1{z^2} = 1 - 2 = -1\)
