Complex Product Nonlinear Equation System
Source: 2012 AIME II Problem 8
March 29, 2012
quadraticscomplex numbersalgebraquadratic formulaAMC
Problem Statement
The complex numbers and satisfy the system
\begin{align*}z+\frac{20i}{w}&=5+i,\\w+\frac{12i}{z}&=-4+10i.\end{align*}
Find the smallest possible value of .