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If |z| = 1, show that 2 ≤ |z^2 – 3| ≤ 4.

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If |z| = 1, show that 2 ≤ |z2 – 3| ≤ 4.

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|z| = 1 ⇒ |z2| = 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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