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Question
If |z| = 1, show that 2 ≤ |z2 – 3| ≤ 4
Solution
|z| = 1
⇒ |z|2 = 1
||z1| – |z2|| ≤ |z1 + z2| ≤ |z1| + |z2|
||z|2 – |– 3|| ≤ |z2 – 3| ≤ |z|2 + |– 3|
|1 – 3| ≤ |z2 – 3| ≤ 1 + 3
2 ≤ |z2 – 3| ≤ 4
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