The Number of complex numbers z such that |z – 1| = |z + 1| = |z – i| equals

• Complex Numbers

The Number of complex numbers z such that |z – 1| = |z + 1| = |z – i| equals

1. 0
2. 1
3. 2
4. infinity

Solution

~ |z – 1| = |z + 1|

lies on y-axis (perpendicular bisector of the line segment joining (0, 1) and (0, -1)

~ |z + 1| = |z – 1|

lies on y = -x

The correct option is B.