I know that $f$ is continuous on $[a,b]$ with $ab\neq0$, $f(a)f(b)\neq0$ and the complex numbers:
$$ z = a^2 + f(a)i $$ $$ w = b^2 - f(b)i $$
$$|\bar w + z| = |w - \bar z|$$
1)Prove that $w\cdot z$ is an imaginary number
2)Calculate the limit $$\lim_{x\to\infty}\frac{f(a)x^3 - f(b)x + 5}{f(b)x^2 + f(a)x - 3}$$