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  • Please help! - Complex numbers and quadratic equations - JEE Main-2

If \left |\frac{1-iz}{z-i} \right |=1 then locus of  z will be 

  • Option 1)

    Real axis

  • Option 2)

    Imaginary axis

  • Option 3)

    Argand plane

  • Option 4)

    Circle

 

Answers (1)

best_answer

\left | \frac{1-iZ}{Z-i} \right |=1\Rightarrow \left | 1-iZ \right |=\left | Z-1 \right |\Rightarrow \left | i \right |\left | \frac{1}{i} -Z\right |=\left | Z-i \right |

\Rightarrow Z lies on perpendicular bisector of line joining i & -i

i.e real axis.

 

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

 

  


Option 1)

Real axis

This is correct

Option 2)

Imaginary axis

This is incorrect

Option 3)

Argand plane

This is incorrect

Option 4)

Circle

This is incorrect

Posted by

prateek

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