Krishna
0

Step 1: Make a note of the equation

               |z + 1 - i| = |z - 1 + i|


Step 2: Simplify the given equation  

                       |z + 1 - i| = |z - 1 + i|

                       |z - (-1 + i)| = |z - (1 - i)|

                                (-1 + i) = (-1, 1)

                                  (1 - i) = (1, -1)

Step 2:  Concluding the shape of the equation.


                  PA = PB, where A denotes the point (–1, 1), B denotes the point (1, –1) and P denotes the point (x, y)

                  z lies on the perpendicular bisector of the line joining A and B and perpendicular bisector is a straight line.