Consider the set of points S={z∈C:∣z−1∣=∣z+i∣}S = \{z \in \mathbb{C} : |z-1| = |z+i|\}S={z∈C:∣z−1∣=∣z+i∣}. Geometrically, this set represents:
A circle with radius 1
A line with slope 1
A line with slope -1
The empty set