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So by simplifying the given expression,
= ∣ z 2 − 2 i z + 1 ∣
= ∣ z 2 − 2 i z + 1 + 1 − 1 ∣
= ∣ z 2 − 2 i z − 1 + 2 ∣
= ∣ ( z − i ) 2 + 2 ∣
As they have given that ∣ z ∣ = 3 , it implies that z lies on a circle of radius 3.
So the distance between z and i must be maximum.
Therefore z = − 3 i .Substituting this in the given expression we get 1 4 .