COMEDK2018MathematicsComplex Number
All complex number z which satisfy the equation | z-6 i z+6 i |=1 lie on the
Options
- Aimaginary axis
- Breal axis
- Cneither of the axes
- 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.