1999 AIME Problem 9

A function f is defined on the complex numbers by f(z)=(a+b i) 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+b i|=8 and that b^{2}=m / n, where m and n are relatively prime positive integers, find m+n.