A function \(f\) is defined on the complex numbers by \(f(z)=(a+bi)z,\) where \(a_{}\) and \(b_{}\) are positive numbers. This function has the property that the image of each point in the complex plane is equidistant from that point and the origin. Given that \(|a+bi|=8\) and that \(b^2=m/n,\) where \(m_{}\) and \(n_{}\) are relatively prime positive integers. Find \(m+n.\)
(第十七届AIME1999 第9题)