MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Properties of Modulus

If |z+2-i|=5,...

Question

If $| z + 2 - i | = 5,$ then the maximum value of $| 3 z + 9 - 7 i |$ is

A

10

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

B

15

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

C

20

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

D

5

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

Open in App

Solution

The correct option is C $20$
Given,
$| z + 2 - i | = 5 \dots (i)$

Now, $| 3 z + 9 - 7 i | = | 3 z + 6 - 3 i + 3 - 4 i |$

We know that,
$| z_{1} + z_{2} | \leq | z_{1} | + | z_{2} |$
$∴ | 3 z + 6 - 3 i + 3 - 4 i | \leq | 3 z + 6 - 3 i | + | 3 - 4 i | \Rightarrow | 3 z + 9 - 7 i | \leq 3 | z + 2 - i | + | 3 - 4 i |$
$\Rightarrow | 3 z + 9 - 7 i | \leq 3 (5) + 5$ [from $(i)$ ]
$\Rightarrow | 3 z + 9 - 7 i | \leq 20$

Suggest Corrections

thumbs-up

13

Similar questions

| z + 2 - i | = 5,

then the maximum value of

| 3 z + 9 - 7 i |

Q. The maximum value of

| 3 z + 9 - 7 i |

| z + 2 - i | = 5

| z + 2 - i | = 5

and maximum value of

| 3 z + 9 - 7 i |

M

, then the value of

\frac{M}{4}

| z + 2 - i | = 5,

then the maximum value of

| 3 z + 9 - 7 i |

| z - 5 - 7 i | = 9,

then find the greatest and least values of

| z - 2 - 3 i | .

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Properties of Modulus

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon