Q18 of 153 Page 14

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


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