Sketching region in the complex plane -- is this correct?

"In the complex plane, sketch the region:

A = { z ∈C | |z - 1| < 3 and Re z ≥ 0 }"

From what I have attempted to work out, I'm stuck between two answers: http://i56.tinypic.com/zodlko.jpg

(Basically, the difference is in terms of the centre of the circle.)

However, I'm still unsure as to whether that is correct or not. I figured the circle, with radius 3 for |z-1| < 3 -- was that correct and which centre would be right? I know that since Re z >= 0, then the region needs to be within the first and fourth quadrants (right?) but is there any way that I should show this or is shading the defined region the right thing to do? Plus, are my graph and axes drawn and labelled correctly? I'm unsure as to whether labelling "Im" for the y-axis was the right thing to do and now, I'm doubting myself with that...