AP EAMCET · Maths · Complex Number
Let \(A(3-i), B(2+i)\) be two points in the argand plane. If the point \(P\) represents the complex number \(z=x+i y\), which satisfies \(|z-3+i|=|z-2-i|\), then the locus of the point \(P\) is
- A the circle with AB as diameter
- B the line passing through A and B
- C the perpendicular bisector of AB
- D the ellipse with AB as major axis
Answer & Solution
Correct Answer
(C) the perpendicular bisector of AB
Step-by-step Solution
Detailed explanation
We have a complex number \(z=x+i y\) \[ \begin{aligned} & \text { and }|z-3+i|=|z-2-i| \\ & \Rightarrow \quad|x+i y-3+i|=|x+i y-2-i| \\ & \Rightarrow \quad(x-3)^2+(y+1)^2=(x-2)^2+(y-1)^2 \\ & \Rightarrow \quad x^3-6 x+9+y^2+2 y+1 \\ & =x^2-4 x+4+y^2-2 y+1 \end{aligned} \]…
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