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

2

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Solution

The correct option is A $2$
$z_{1}_{1} = 1, z_{2}_{2} = 4, z_{3}_{3} = 9$
$Given | 9 z_{1} z_{2} + 4 z_{1} z_{3} + z_{2} z_{3} | = 12$
$\Rightarrow | z_{3}_{3} z_{1} z_{2} + z_{2}_{2} z_{1} z_{3} + z_{1}_{1} z_{2} z_{3} | = 12$
$\Rightarrow | z_{1} | | z_{2} | | z_{3} | |_{1} +_{2} +_{3} | = 12$
$\Rightarrow 6 | z_{1} + z_{2} + z_{3} | = 12 (∵ |_{1} +_{2} +_{3} | = | z_{1} + z_{2} + z_{3} |)$
$\Rightarrow | z_{1} + z_{2} + z_{3} | = 2$

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Similar questions

Q. 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 the value of

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

is equal to

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

Q. 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 the value of

| 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:

∣ 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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If |z1|=1,|z2|=2,|z3|=3 and |9z1z2+4z1z3+z2z3|=12, then the value of |z1+z2+z3| is equal to

The correct option is A 2z1¯z1=1, z2¯z2=4, z3¯z3=9 Given |9z1z2+4z1z3+z2z3|=12 ⇒|z3¯z3z1z2+z2¯z2z1z3+z1¯z1z2z3|=12 ⇒|z1||z2||z3||¯z1+¯z2+¯z3|=12 ⇒6|z1+z2+z3|=12 (∵|¯z1+¯z2+¯z3|=|z1+z2+z3|) ⇒|z1+z2+z3|=2

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