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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 $$\lim_{x\to\infty}\frac{f(a)x^3 - f(b)x + 5}{f(b)x^2 + f(a)x - 3}$$

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    By $a*b!=0$ you mean $a*b\neq 0$, correct? The LaTeX for $\neq$ is "\neq"2012-12-16
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    i squared the 3rd equation and got to w conjugate * z conjugate + wz = 02012-12-16
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    @Nick Then you are almost done - what does $\overline {wz}=-wz$ imply?2012-12-16
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    @Nick If you've figured it out, [feel free to post an answer (and accept it)](http://meta.math.stackexchange.com/questions/2637/policy-on-accepting-my-own-answer).2012-12-17

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