z & w are variable complex numbers satisfying \left |z \right |= 2 and \left |w \right |= 3 then maximum possible value of \left |z+w \right | equals

  • Option 1)

    4

  • Option 2)

    5

  • Option 3)

    6

  • Option 4)

    7

 

Answers (1)
P Plabita

\left | z+w \right |\leq \left | z \right |+\left | w \right |

\Rightarrow \left | z+w \right |\leq 2+3\Rightarrow \left | z+w \right |\leq 5

\therefore \left | z+w \right | have maximum value 5

\therefore Option (B)

 

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)

4

This is incorrect

Option 2)

5

This is correct

Option 3)

6

This is incorrect

Option 4)

7

This is incorrect

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