Let S = z C : |z - (1+i)| = |z - (3+3i)| = |z - (4+4i)| . Then, n(S) is equal to:

Step-by-step solution

The given equation implies that the complex number z is equidistant from the three points A(1,1) , B(3,3) , and C(4,4) in the complex plane. Observe that the points A , B , and C lie on the same straight line y = x . The locus of points equidistant from A and B is the perpendicular bisector of the line segment AB . Similarly, the locus of points equidistant from B and C is the perpendicular bisector of the line segment BC . Since A , B , and C are distinct and collinear, their perpendicular bisectors are parallel t