# Minimizing more than one variable

Algebra Level pending

A Function $$f(z)=(4+i){ z }^{ 2 }+\alpha z+\gamma$$, ($$\alpha ,\gamma \in C$$) is such that both $$f(1)$$ and $$f(i)$$ are pure real quantities. Let the minimum value of $$\left| \alpha \right| +\left| \gamma \right| =k$$ , Compute $$\left[ \frac { { k }^{ 2 } }{ 2 } \right]$$ ($$\left[ . \right]$$ denotes GIF).

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