1999 AIME Problems/Problem 9

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Problem

A function $\displaystyle f$ is defined on the complex numbers by $\displaystyle f(z)=(a+bi)z,$ where $\displaystyle a_{}$ and $\displaystyle b_{}$ 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 $\displaystyle |a+bi|=8$ and that $\displaystyle b^2=m/n,$ where $\displaystyle m_{}$ and $\displaystyle n_{}$ are relatively prime positive integers. Find $\displaystyle m+n.$

Solution

See also