The equation |z+1-i|=|z-1+i| represents a (where z is a complex number)

Step-by-step solution

Let z = x + iy . The equation |z+1-i| = |z-1+i| represents points equidistant from -1+i and 1-i . Substituting z = x + iy gives: |(x+1) + i(y-1)| = |(x-1) + i(y+1)| Squaring both sides eliminates the radicals: (x+1)^2 + (y-1)^2 = (x-1)^2 + (y+1)^2 Expanding yields: x^2 + 2x + 1 + y^2 - 2y + 1 = x^2 - 2x + 1 + y^2 + 2y + 1 Subtracting x^2 + y^2 + 2 from both sides simplifies to: 2x - 2y = -2x + 2y Solving gives 4x = 4y , so x = y . The line y = x passes through the origin and makes equal angles with the axes, lying