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If ∣z + 4∣ ≤ 3, then the greatest and the least value of ∣z + 1∣ are

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∣z + 4∣ ≤ 3 ⇒−3 ≤ z + 4 ≤ 3

⇒−6 ≤ z + 1 ≤ 0

⇒0 ≤ −(z + 1) ≤ 6

⇒0 ≤ ∣z + 1∣ ≤ 6 

Hence, the greatest and least values are 6 and 0.

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