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Q.
The equation $|z+1-i|=|z-1+i|$ represents a
Complex Numbers and Quadratic Equations
Solution:
$|z+1-i|=|z-1+i|$
$\Rightarrow |z-(-1+i)|=|z-(1-i)|$
$\Rightarrow P A=P B$, where $A$ denotes the point $(-1,1), B$ denotes the point $(1,-1)$ and $P$ denotes the point $(x, y)$.
$\Rightarrow z$ lies on the perpendicular bisector of the line joining $A$ and $B$ and perpendicular bisector is a straight line.