1999 AIME Problem 9

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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.