The locus of the point Z satisfying the condition $$arg \frac{z - 1}{z + 1} = \frac {\pi}{3}$$ is

A

$$x^2 - y^2 - 2 \sqrt {3} y = 0$$

B

$$x^2 + y^2 = 1$$

C

$$x^2 - y^2 - 2 \sqrt {3} y - 1 = 0$$

D

$$x^2 + y^2 - 2 \sqrt {3} y - 1 = 0$$