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  • I need help with - Complex numbers and quadratic equations - JEE Main-8

z is a variable complex number which satisfies \left |z \right |= 2  then maximuim possible value of \left |z+2 \right | equals

  • Option 1)

    1

  • Option 2)

    2

  • Option 3)

    3

  • Option 4)

    4

 

Answers (1)

best_answer

We know, \left | z_{1}+z_{2} \right |\leq \left | z_{1} \right |+\left | z_{2} \right |

Here, z_{1}=z\: and\: z_{2}=2,\: So

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

It means maximum value of \left | z+2 \right | is 4

\therefore Option (D)

 

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)

1

This is incorrect

Option 2)

2

This is incorrect

Option 3)

3

This is incorrect

Option 4)

4

This is correct

Posted by

Himanshu

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