I think this should probably be easy, but I am stuck. My book is of no help. Find and describe the locus of points z satisfying the given equations: 1. |z-i|=Re z 2. |z-1|^2 =|z+1|^2 +6 I am thinking for the 1st one that I have to square both sides, but then what? What happens to Re z? For the second one, I am totally lost. My first instinct would be to take the square root of both sides...and then...? Thanks to all.