If the complex number Z is on the circle | Z | = 2, then it is proved that: | 1 / (Z ^ 4-4z ^ 2 + 3)| | Math enthusiast | Mathematical art

If the complex number Z is on the circle | Z | = 2, then it is proved that: | 1 / (Z ^ 4-4z ^ 2 + 3)|

Because Z ^ 4-4z ^ 2 + 3 = (Z ^ 2-1) (Z ^ 2-3),
And | Z ^ 2-1 | > = | Z ^ 2 | - 1 = 3, | Z ^ 2-3 | > = | Z ^ 2 | - 3 = 1,
So | Z ^ 4-4z ^ 2 + 3 | > = 3,
So | 1 / (Z ^ 4-4z ^ 2 + 3)|

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