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  • Help me solve this - Complex numbers and quadratic equations - JEE Main-11

The number of complex numbers z such that

\left | z-1 \right |= \left | z+1 \right |= \left | z-i \right | equals

  • Option 1)

    0

  • Option 2)

    1

  • Option 3)

    2

  • Option 4)

    \infty

 

Answers (2)

best_answer

As we have learned

Perpendicular bisector -

Locus of point equidistant from two given points.

\left |z-z_{1} \right |=\left |z-z_{2} \right |

z will lie on perpendicular bisector of line joining z_{1} and z_{2} .

- wherein

z_{1} and z_{2} are any two fixed points . z is a moving point in the plain which is equidistant from z_{1} and z_{2} .so z will lie on perpendicular bisector

 

 

So ,  x= 0 

and  y = x

are the lines which intersect at origin (0) 

No. of values of z = 1

 

 

 

 

 


Option 1)

0

Option 2)

1

Option 3)

2

Option 4)

\infty

Posted by

Himanshu

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