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Manipal MET2018MathematicsComplex Number

The complex number z which satisfy the equation | i+z i-z |=1 lies on

Options

  1. Aa circle x^2+y^2=1
  2. Bthe x -axis
  3. Cthe y -axis
  4. Dthe line x+y=1

Correct answer

B. the x -axis

Step-by-step solution

Let z=x+i y aligned & & i+z & =x+i(1+y) & and & i-z & =-x+i(1-y) & & & | i+z i-z | aligned array cc & x^2+(1+y)^2=x^2+(1-y)^2 & x^2+y^2+2 y+1=x^2+y^2+1-2 y & 4 y=0 & y=0 array i.e. x -axis.

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