the locus of the complex number z such that Iz+3I = Iz-1I is?
A.     A line
B.     A circle
C.     A quadratic curve
An ellipseÂ
Given that "|z+3|=|z-1|"
Let "z=x+iy"
"|x+iy+3|=|x+iy-1|\\\\\n\\Rightarrow \\sqrt{(x+3)^2+y^2}=\\sqrt{(x-1)^2+y^2}\\\\"
Squaring both sides, we get:
"(x+3)^2+y^2=(x-1)^2+y^2\\\\\n\\Rightarrow x^2+9+6x=x^2+1-2x\\\\\n\\Rightarrow 8x+8=0\\\\\n\\Rightarrow x=-1"
Therefore, the locus of a given complex number is a line.
Hence, the correct option is (A).
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