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

• A

  $4$
• B

  $10$
• Correct answer
  C

  $6$
• D

  $0$

Solution

From the Argand diagram maximum value of $|z+1|$ is $6$. Alternative: $\begin{aligned} & |z+1|=|z+4-3| \\ & \leq|z+4|+|-3|=6. \end{aligned}$

Hence, the correct answer is option: 'C'.