Please explain to me why:
$$ Z^2 = \bar{Z} $$

Has a 3rd and 4th solutions: $1, 0$ ?

I found the first two complex numbers, but why also $1$ and $0$ ? 

I replaced $Z^2$ with $(x+yi)^2$ and $\bar{Z}$ with $x-yi$ .
Why did I only find the first two solutions? What am I missing?