If |z + 4| ≤ 3, then find the greatest and least values of |z + 1|.
6 and 0
Explanation
As we all know that,
|z1 +z2 |≤|z1 |+|z2 | and |z1 +z2 |≥|z1 |-|z2 |
Suppose,
Z1 = z+4
Z2 = -3
| z1|-| z2|≤| z1+ z2|≤ | z1|+| z2|
|z+4|-|-3|≤|z+4-3|≤ |z+4|+|-3|
|z+4|-3≤|z+1|≤ |z+4|+3
3-3≤|z+1|≤ 3+3 (Given-|z + 4| ≤ 3)
0≤|z+1|≤ 6