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 $x^{2} + (y+2)^{2} = 1$

For the complex number $z = a + ib$ whose distance to the number 1 is 2 units and whose distance to the number i is 3 units, what is the difference $a - b$?
A) $\frac { 3 } { 2 }$
B) $\frac { 5 } { 2 }$
C) $\frac { 7 } { 2 }$
D) $\frac { 4 } { 3 }$
E) $\frac { 7 } { 3 }$