1. The problem statement, all variables and given/known data Let z=x+iy. Describe the locus of points z satisfying |z-i|=Re(z). 2. Relevant equations N/A 3. The attempt at a solution |z-i|=Re(z) => sqrt[x2+(y-1)2] = x => x2+(y-1)2 = x2 => (y-1)2 = 0 => y=1 But the answer says y=1 and x≥0. Why? I think maybe I'm not getting the x≥0 because my implcations above isn't "if and only if". But what exactly is the reason and how can we rigorously justify that x≥0? Any help is appreciated!