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

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Question: Answered & Verified by Expert

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

MathematicsComplex NumberJEE Main

Options:

A \( 4 \)
B \( 10 \)
C \( 6 \)
D \( 0 \)

Solution:

2882 Upvotes Verified Answer

The correct answer is: \( 6 \)

From the argand diagram, maximum value of $|z + 1|$ is $6$ .
Aliter
$|z + 1| = |z + 4 - 3| \leq |z + 4| + |- 3| \leq 6$
Thus, maximum value of $|z + 1|$ is $6$ .

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