Question

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

Answer 1

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.]