Mixing of concepts!

Calculus Level 5

A function is defined as f(x)=ax4+bx3+cx2+dx+λ f(x)=ax^4+bx^3+cx^2+dx+\lambda. This function has a special property: f(1)1=f(2)2=f(3)3\dfrac{f(1)}{1}=\dfrac{f(2)}{2}=\dfrac{f(3)}{3}. If limxf(x)x4=1\displaystyle \lim _{ x\to \infty }{ \dfrac { f( x ) }{ { x }^{ 4 } } } =1, then find f(i)+f(i)f(i)+f(-i) where i=1i=\sqrt{-1}.

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