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  • Solve it, - Complex numbers and quadratic equations - JEE Main-7

z is a complex number always satisfying \left |z-i \right |= 2  then minimum possible value of \left |z-3-5i \right | equals

  • Option 1)

    1

  • Option 2)

    2

  • Option 3)

    3

  • Option 4)

    4

 

Answers (1)

best_answer

\left | z-3-5i \right |=\left | \left ( z-i \right )-\left ( 3+4i \right ) \right |\geq \left | \left | z-i \right |-\left | 3+4i \right | \right |

                                     z_{1}                 z_{2}

\Rightarrow \left | z-3-5i \right |\geq \left | 2-5 \right |\Rightarrow \left | z-3-5i \right |\geq 3

\therefore Option (C)

 

Triangle Law of Inequality in Complex Numbers -

|z_{1}-z_{2}|\geq \left || z_{1} \right |-| z_{2} \right |||

- wherein

|.| denotes modulus of z in complex numbers

 

 


Option 1)

1

This is incorrect

Option 2)

2

This is incorrect

Option 3)

3

This is correct

Option 4)

4

This is incorrect

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