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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Solution

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

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

$| 9 \times 1 \times - 2 + 4 \times 1 \times 3 + - 2 \times 3 | = 12$

$| - 18 + 12 - 6 | = 12$

$| - 24 + 12 | = 12$

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

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

∣ 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} ∣

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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If |z1|=1,|z2|=2,|z3|=3 and |9z1z2+4z1z3+z2z3|=12, then find the value of |z1+z2+z3|.

|z1|=1, |z2|=2,|z3|=3|9z1z2+4z2z3+z2+z3|=12 |9×1×−2+4×1×3+−2×3|=12|−18+12−6|=12|−24+12|=12|9z1+4z2z3+z2+z3|=12 satisfies only when z1=1,z2=−2 and z3=3Therefore z1=1,z2=−2 and z3=3 So , The value of |z1+z2+z3|=|1−2+3| =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 find the value of $| z_{1} + z_{2} + z_{3} |$ .