Complex Numbers

Let \(\mathrm{z_1=2+3i}\) and \(\mathrm{z_2=3+4i}\). The set \(\mathrm{S = \left\{ {z \in \mathbb{C}:{{\left| {z - {z_1}} \right|}^2} - {{\left| {z - {z_2}} \right|}^2} = {{\left| {{z_1} - {z_2}} \right|}^2}} \right\}}\) represents a