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If |z_{1}| = 1, |z_{2}| = 2, |z_{3}| = 3 and |9z_{1}z_{2} + 4z

Question

If $∣ z_{1} ∣ = 1, ∣ z_{2} ∣ = 2, ∣ z_{3} ∣ = 3$ and $∣9 z_{1} z_{2} + 4 z_{1} z_{3} + z_{2} z_{3} ∣ = 12$ , then find the value of $∣ z_{1} + z_{2} + z_{3} ∣$ .

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Lucas Discussed

∣ z_{1} ∣ = 1, ∣ z_{2} ∣ = 2, ∣ z_{3} ∣ = 3

and

∣9 z_{1} z_{2} + 4 z_{1} z_{3} + z_{2} z_{3} ∣ = 12

, then find the value of

∣ z_{1} + z_{2} + z_{3} ∣

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Text solutionVerified

∣ z_{1} ∣ = 1

∣ z_{2} ∣ = 2

∣ z_{3} ∣ = 3

∣9 z_{1} z_{2} + 4 z_{2} z_{3} + z_{2} + z_{3} ∣ = 12

∣9 \times 1 \times - 2 + 4 \times 1 \times 3 + - 2 \times 3∣ = 12

∣ - 18 + 12 - 6∣ = 12

∣ - 24 + 12∣ = 12

∣9 z_{1} + 4 z_{2} z_{3} + z_{2} + z_{3} ∣ = 12

satisfies only when

z_{1} = 1

z_{2} = - 2

and

z_{3} = 3

Therefore

z_{1} = 1

z_{2} = - 2

and

z_{3} = 3

So , The value of

∣ z_{1} + z_{2} + z_{3} ∣ = ∣1 - 2 + 3∣

= 2

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Question Text	If $∣ z_{1} ∣ = 1, ∣ z_{2} ∣ = 2, ∣ z_{3} ∣ = 3$ and $∣9 z_{1} z_{2} + 4 z_{1} z_{3} + z_{2} z_{3} ∣ = 12$ , then find the value of $∣ z_{1} + z_{2} + z_{3} ∣$ .
Answer Type	Text solution:1
Upvotes	150