If $| z + 4 | \leq 3$ , then the maximum value of $| z + 1 |$ is

4

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6

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10

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0

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Solution

The correct option is C $6$
$| z + 1 | = | (z + 4) + (- 3) |$
$| z + 1 | \leq | z + 4 | + | - 3 |$
$| z + 1 | \leq 3 + 3$
Using triangle inequality
$| z + 1 | \leq 6$
Max. $| (z + 1) | = 6$

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