A function \(f\) is defined on the complex numbers by \(f(z) = (a+bi)z,\) where \(a\) and \(b\) are positive real numbers. Each point in the image of \(f\) is equidistant from the point \(z\) and the origin. Given that \(|a+bi| = 8,\) find \(a\) and \(b.\)

Guest Dec 15, 2019