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COMEDK2018MathematicsComplex Number

All complex number z which satisfy the equation | z-6 i z+6 i |=1 lie on the

Options

  1. Aimaginary axis
  2. Breal axis
  3. Cneither of the axes
  4. DNone of the above

Correct answer

B. real axis

Step-by-step solution

We have, aligned & | z-6 i z+6 i |=1 & or |z-6 i|=|z+6 i| & Let z=x+i y & or |x+i y-6 i|=|x+i y+6 i| & |x+(y-6) i|=|x+(y+6) i| & x²+(y-6)² = x²+(y+6)² & x²+(y-6)²=x²+(y+6)² & y²+36-12 y=y²+36+12 y & 24 y=0 & y=0 aligned Hence, it is lie on the real axis.

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