If $|z + 4|$ less than or equal to $3$ , then the maximum value of $|z + 1|$ is

$4$

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$10$

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$6$

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$0$

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Solution

The correct option is C
$6$

The explanation for the correct option
It is given that $|z + 4|$ less than or equal to $3$ .
Thus, $|z + 4| \leq 3$ .
Now, $|z + 1| = |z + 4 - 3|$
$\Rightarrow |z + 1| = |(z + 4) + (- 3)|$
It is known that, $|a + b| \leq |a| + |b|$ .
Thus, $|z + 1| \leq |z + 4| + |- 3|$
$\Rightarrow |z + 1| \leq 3 + 3 [∵ |z + 4| \leq 3] \Rightarrow |z + 1| \leq 6$
Thus, the maximum value of $|z + 1|$ is $6$ .
Hence, (C) is the correct option.

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