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Found problems: 1

2017 AIME Problems, 10
Tags: 2017 AIME 1 problem 10 , Wot n
Let $z_1 = 18 + 83i$, $z_2 = 18 + 39i, $ and $z_3 = 78 + 99i,$ where $i = \sqrt{-1}$. Let $z$ be the unique complex number with the properties that $\frac{z_3 - z_1}{z_2 - z_1} \cdot \frac{z - z_2}{z - z_3}$ is a real number and the imaginary part of $z$ is the greatest possible. Find the real part of $z$.