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Properties of Conjugate of a Complex Number

| z 1|=1,| z ...

Question

$| z_{1} | = 1, | z_{2} | = 2, | z_{3} | = 3 a n d | 9 z_{1} z_{2} + 4 z_{1} z_{3} + z_{2} z_{3} | = 12$ , then the value of $| z_{1} + z_{2} + z_{3} |$ is equal to

A

2

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B

3

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C

4

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D

6

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Solution

The correct option is A
2

$| z_{1} | = 1, \Rightarrow z_{1}_{1} = 1 | z_{2} | = 2, \Rightarrow z_{2}_{2} = 4 | z_{3} | = 3, \Rightarrow z_{3}_{3} = 9 | 9 z_{1} z_{2} + 4 z_{1} z_{3} + z_{2} z_{3} | = 12 \Rightarrow ∣ ∣ z_{1} z_{2} z_{3}_{3} + z_{1} z_{2} z_{3}_{2} + z_{1}_{1} z_{2} z_{3} ∣ ∣ = 12 \Rightarrow | z_{1} z_{2} z_{3} | ∣ ∣_{1} +_{2} +_{3} ∣ ∣ = 12 \Rightarrow | z_{1} | | z_{2} | | z_{3} | ∣ ∣_{1} +_{2} +_{3} ∣ ∣ = 12 \Rightarrow 6 ∣ ∣_{1} +_{2} +_{3} ∣ ∣ = 12 \Rightarrow ∣ ∣_{1} +_{2} +_{3} ∣ ∣ = 2 | z_{1} + z_{2} + z_{3} | = 2$

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Similar questions

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

| 9 z_{1} z_{2} + 4 z_{1} z_{3} + z_{2} z_{3} | = 12,

then the value of

| z_{1} + z_{2} + z_{3} |

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

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

then the value of

| z_{1} + z_{2} + z_{3} |

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

| 9 z_{1} z_{2} + 4 z_{1} z_{3} + z_{2} z_{3} | = 12,

then the value of

| z_{1} + z_{2} + z_{3} |

∣ z_{1} ∣= 1

∣ z_{2} ∣= 2

∣ z_{3} ∣= 3

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

∣ z_{1} + z_{2} + z_{3} ∣

If | $z_{1}$ | = 1, | $z_{2}$ | = 2, | $z_{3}$ | = 3 and | $9 z_{1} z_{2} + 4 z_{1} z_{3}$ | = 12, then the value of | $z_{1}$ + $z_{2}$ + $z_{3}$ | is equal to:

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