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If |z| < 4, prove that |i z + 3 – 4i| < 9.

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If |z| < 4, prove that |i z + 3 – 4i| < 9.
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 |Z| < 4

|3 + i(Z – 4)| < 9(To prove)

We know that |Z1 + Z2| ≤  |Z1| + |Z2|

|iZ + (3 – 4i)| ≤  |Z| + |3 – i4

Z| < 4

⇒|iZ + (3 – 4i)| < 4 + 5

⇒|iZ + (3 – 4i)| < 9 Hence proved

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