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If $| z_{1} | = 2, | z_{2} | = 3, | z_{3} | = 4 & | 16 z_{1} z_{2} + 9 z_{1} z_{3} + 4 z_{2} z_{3} |$ = 96 then $| z_{1} + z_{2} + z_{3} | =$

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Detailed Solution

$z_{1} {\bar{z}}_{1} = 4, z_{2} {\bar{z}}_{2} = 9, z_{3} {\bar{z}}_{3} = 16$

$| 16 z_{1} z_{2} + 9 z_{1} z_{3} + 4 z_{2} z_{3} | = | z_{3} {\bar{z}}_{3} z_{1} z_{2} + z_{2} {\bar{z}}_{2} z_{1} z_{3} + z_{1} {\bar{z}}_{1} z_{2} z_{3} | = 96$

$\Rightarrow | z_{1} | | z_{2} | | z_{3} | | {\bar{z}}_{1} + {\bar{z}}_{2} + {\bar{z}}_{3} | = 96 \Rightarrow | z_{1} + z_{2} + z_{3} | = 4$

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