A) \[2x+4y-5=0\]
B) \[2x-4y-5=0\]
C) \[x+2y=0\]
D) \[x-2y+5=0\]
Correct Answer: A
Solution :
\[|z-2+i|\,=\,|z-3-i|\] \[\Rightarrow \] \[|(x-2)+i(y+1)|\] \[=\,|(x-3)\,+i\,(y-1)|\] \[\Rightarrow \] \[\sqrt{{{(x-2)}^{2}}+{{(y+1)}^{2}}}\]=\[\sqrt{{{(x-3)}^{2}}+{{(y-1)}^{2}}}\] \[\Rightarrow \] \[{{x}^{2}}+4-4x+{{y}^{2}}+1+2y={{x}^{2}}+9-6x+{{y}^{2}}+1-2y\] \[\Rightarrow \] \[2x+4y-5=0\].
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