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)