Sketching complex numbers with only the imaginary part

Question

How can sketch complex numbers given only the Imaginary part?

For example, sketch all complex numbers such that Im(z) = |z − i/2|

Answer 1

If $z=x+iy,$ then you have the equation $$y=|x+i(y-1/2)|=\sqrt{x^2+(y-1/2)^2}.$$ All that you need to do is figure out how to sketch this!