$∣ z_{1} ∣= 1$ , $∣ z_{2} ∣= 2$ , $∣ z_{3} ∣= 3$
and $∣ 9 z_{1} z_{2} + 4 z_{3} z_{1} + z_{2} z_{3} ∣= 12$
Find: $∣ z_{1} + z_{2} + z_{3} ∣$ .

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Solution

$z_{1}_{1} = | z_{1} |^{2} = 1$ $, z_{2}_{2} = | z_{2} |^{2} = 4$ $, z_{3}_{3} = | z_{3} |^{2} = 9$
$| z_{2} z_{3} + 4 z_{3} z_{1} + 9 z_{1} z_{2} | = 12$
$⟹ |_{1} z_{1} z_{2} z_{3}$ $+_{2} z_{1} z_{2} z_{3}$ $+_{3} z_{1} z_{2} z_{3} | = 12$
$⟹ | z_{1} | | z_{2} | | z_{3} | |_{1} +_{2} +_{3} | = 12$
$⟹ 6 \times$ $|_{1} +_{2} +_{3} | = 12$
$⟹ |_{1} +_{2} +_{3} | = 2$

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∣z1∣=1, ∣z2∣=2 ,∣z3∣=3 and ∣9z1z2+4z3z1+z2z3∣=12Find: ∣z1+z2+z3∣.

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$∣ z_{1} ∣= 1$ , $∣ z_{2} ∣= 2$ , $∣ z_{3} ∣= 3$
and $∣ 9 z_{1} z_{2} + 4 z_{3} z_{1} + z_{2} z_{3} ∣= 12$
Find: $∣ z_{1} + z_{2} + z_{3} ∣$ .