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NDA2023MathematicsComplex NumberActual

If z z =|z+ z | , where z=x+i y, i= -1 then the locus of z is a pair of :

Options

  1. AStraight lines
  2. Brectangular hyperbolas
  3. Cparabolas
  4. Dcircles

Correct answer

D. circles

Step-by-step solution

aligned & Since, z = x + iy & Now, ( x + iy )( x - iy )=| x + iy + x - iy | & x ^2-( iy )^2=|2 x | & x ^2+ y ^2=2 x x ^2-2 x +1+ y ^2=1 & ( x -1)^2+ y ^2=1 aligned So locus of z is circle

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