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  • Help me understand! - Complex numbers and quadratic equations - JEE Main-11

z is a variable complex number satisfying \left |z-1 \right |= 2 then maximum possible value of \left |z+2+4i \right | equals

  • Option 1)

    5

  • Option 2)

    6

  • Option 3)

    7

  • Option 4)

    8

 

Answers (1)

\left | z+2+4i \right |=\left | \left ( z-1 \right )+\left ( 3+4i \right ) \right | 

                                     z_{1}                   z_{2}

\because \left | z_{1}+z_{2} \right |\leq \left | z_{1} \right |+\left | z_{2} \right |

\therefore \left | \left ( z-1 \right )+\left ( 3+4i \right ) \right |\leq \left | z-1 \right |+\left | 3+4i \right |

\Rightarrow \left | z+2+4i \right |\leq 2+5

\Rightarrow \left | z+2+4i \right |\leq 7

\therefore Maximum value of \left | z+2+4i \right |=7

\therefore Option(C)

 

Triangle Law of Inequality in Complex Numbers -

\left | z_{1}+z_{2} \right |\leq \left | z_{1} \right |+\left | z_{2} \right |

- wherein

|.| denotes modulus of complex number.

 

 


Option 1)

5

This is incorrect

Option 2)

6

This is incorrect

Option 3)

7

This is correct

Option 4)

8

This is incorrect

Posted by

Vakul

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