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NDA2021MathematicsComplex NumberActual

If z=x+i y , where i= -1 , then what does the equation z z +|z|^2+4(z+ z )-48=0 represent?

Options

  1. AStraight line
  2. BParabola
  3. CCircle
  4. DPair of straight lines

Correct answer

C. Circle

Step-by-step solution

Here z=x+i y z =x-i y aligned & z z +|z|^2+4(z+ z )-48=0 & |z|^2+|z|^2+4(z+ z )-48=0 [ z z =|z|^2 ] & 2 (x^2+y^2 )+4(2 x)-48=0 & x^2+y^2+4 x-48=0 aligned Represent equation of circles.

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