Let z be a complex number such that z + 1/z = -1. Find z^3.
z + 1/z = -1
(z + 1/z)^3 = -1
z^3 + 3z + 3/z + 1/z^3 = -1
z^3 + 3(z + 1/z) + 1/z^3 = -1
z^3 + 3(-1) + 1/z^3 = -1
z^3 + 1/z^3 = 2
can you take it from here?
=^._.^=
