If z is a complex number satisfying z + 1/z = 1, calculate z^2 + 1/z^2.
\(\phantom{z^10 + 1/z^10}\)
\(\phantom{z^3 + 1/z^3}\)
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
