AP EAMCET · Maths · Complex Number
The locus of the point representing the complex number \(z\) for which \(|z+3|^2-|z-3|^2=15\) is
- A a circle
- B a parabola
- C a straight line
- D an ellipse
Answer & Solution
Correct Answer
(C) a straight line
Step-by-step Solution
Detailed explanation
Let the comlex number, \(z=x+i y\) Now, \(|z+3|^2-|z-3|^2=15\) \(\begin{aligned} & \therefore \quad|x+i y+3|^2-|x+i y-3|^2=15 \\ & (x+3)^2+y^2-(x-3)^2-y^2=15 \\ & x^2+6 x+9-x^2+6 x-9=15 \\ & 12 x=15 \Rightarrow 4 x=5 \end{aligned}\) \(\therefore\) It represents a straight line.
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