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  • Give answer! - Complex numbers and quadratic equations - JEE Main-5

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

  • Option 1)

    2

  • Option 2)

    3

  • Option 3)

    4

  • Option 4)

    5

 

Answers (1)

best_answer

We know,

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

\Rightarrow \left | z-2 \right |\geq \left | \left | z \right |-\left | 2 \right | \right |

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

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

\therefore \left | z-2 \right | has minimum possible value 3

\therefore Option (B)

 

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)

2

This is incorrect

Option 2)

3

This is correct

Option 3)

4

This is incorrect

Option 4)

5

This is incorrect

Posted by

Aadil

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