# 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) $7$

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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