Question
Question: If z is any complex number such that \| z + 4 \| £ 3, then the least value and greatest value of \| ...
If z is any complex number such that | z + 4 | £ 3, then the least value and greatest value of | z + 1| are
A
1, 6
B
0, 6
C
2, 8
D
None of these
Answer
0, 6
Explanation
Solution
Sol. Least value of | z + 1| is 0 and this happens when z = – 1
Ž | z + 4| = | – 1 + 4 | = 3 £ 3 | z + 1|
= | (z + 4) – 3 | £ | z + 4 | + | – 3 |
£ 3 + 3 £ 6
greatest value of | z + 1 | = 6