Mixing of concepts!

Calculus Level 5

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

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