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A function f is defined by f(z) = (4 + i)*z^2 + \alpha z + \gamma for all complex numbers z, where \alpha and \gamma are complex numbers and i^2 = - 1. Suppose that f(1) and f(i) are both real. What is the smallest possible value of | alpha | + | gamma |? (The | | are absolute values).

 Sep 6, 2020
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The smallest possible value of |alpha| + |beta| is 2 + sqrt(3).

 Sep 6, 2020

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