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AP EAMCET2016MathematicsComplex Number

The locus of the point representing the complex number z for which |z+3|^2-|z-3|^2=15 is

Options

  1. Aa circle
  2. Ba parabola
  3. Ca straight line
  4. Dan ellipse

Correct answer

C. a straight line

Step-by-step solution

Let the comlex number, z=x+i y Now, |z+3|^2-|z-3|^2=15 aligned & |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 4 x=5 aligned It represents a straight line.

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