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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

6

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $2$
$| z_{1} | = 1, | z_{2} | = 2, | z_{3} | = 3$
$| 9 z_{1} z_{2} + 4 z_{1} z_{3} + z_{2} z_{3} | = 12$
$\Rightarrow | | z 3 |^{2} z_{1} z_{2} + | z_{2} |^{2} z_{1} z_{3} + | z_{1} |^{2} z_{2} z_{3} | = 12$
$\Rightarrow | z_{1} z_{2} z_{3} {¯ ¯ ¯ z}_{3} + z_{1} z_{2} z_{3} {¯ ¯ ¯ z}_{2} + z_{1} z_{2} z_{3} {¯ ¯ ¯ z}_{1} | = 12$
$\Rightarrow | z_{1} z_{2} z_{3} | | {¯ ¯ ¯ z}_{1} + {¯ ¯ ¯ z}_{2} + {¯ ¯ ¯ z}_{3} | = 12$
$\Rightarrow | z_{1} | | z_{2} | | z_{3} | | ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ z_{1} + z_{2} + z_{3} | = 12$
$\Rightarrow | z_{1} + z_{2} + z_{3} | = 2$

Suggest Corrections

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

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} |

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

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} ∣

Join BYJU'S Learning Program

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 2|z1|=1,|z2|=2,|z3|=3|9z1z2+4z1z3+z2z3|=12⇒||z3|2z1z2+|z2|2z1z3+|z1|2z2z3|=12⇒|z1z2z3¯¯¯z3+z1z2z3¯¯¯z2+z1z2z3¯¯¯z1|=12⇒|z1z2z3||¯¯¯z1+¯¯¯z2+¯¯¯z3|=12⇒|z1||z2||z3||¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯z1+z2+z3|=12⇒|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