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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

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B

15

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C

20

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D

5

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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 $(i)$ ]
$\Rightarrow | 3 z + 9 - 7 i | \leq 20$

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Similar questions

| z + 2 - i | = 5,

then the maximum value of

| 3 z + 9 - 7 i |

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| 3 z + 9 - 7 i |

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Properties of Modulus

Standard XII Mathematics

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