MathDB

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.

Problem Statement