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If |z + 4| ≤ 3, then the greatest and least values of |z + 1| are ______ and ______.

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#### Solution

If |z + 4| ≤ 3, then the greatest and least values of |z + 1| are **6** and **0**.

**Explanation:**

Given that: |z + 4| ≤ 3

For the greatest value of |z + 1|.

= |z + 4 – 3| ≤ |z + 4| + |–3|

= |z + 4 – 3| ≤ 3 + 3 ......[∵ |z + 4| ≤ 3 and |–3| = 3]

= |z + 4 – 3| ≤ 6

Hence, the greatest value of |z + 1| is 6 and for the least value of |z + 1| = 0. .....[∵ The least value of the modulus of complex number is 0.]

Concept: Algebraic Operations of Complex Numbers

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