In the complex number plane $$|z-1| = |z+2|$$ Which of the following does this equation represent?
A) The line $x = 1$
B) The line $x = \frac{-1}{2}$
C) The line $x = 2$
D) The circle $(x-1)^{2} + y^{2} = 1$
E) The circle $x^{2} + (y+2)^{2} = 1$
In the complex number plane
$$|z-1| = |z+2|$$
Which of the following does this equation represent?

A) The line $x = 1$\\
B) The line $x = \frac{-1}{2}$\\
C) The line $x = 2$\\
D) The circle $(x-1)^{2} + y^{2} = 1$\\
E) The circle $x^{2} + (y+2)^{2} = 1$