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Question
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.]
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