MathDB
Wot n' Imagination

Source: 2017 AIME I #10

March 8, 2017
2017 AIME 1 problem 10Wot n

Problem Statement

Let z1=18+83iz_1 = 18 + 83i, z2=18+39i,z_2 = 18 + 39i, and z3=78+99i,z_3 = 78 + 99i, where i=−1i = \sqrt{-1}. Let zz be the unique complex number with the properties that z3−z1z2−z1⋅z−z2z−z3\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 zz is the greatest possible. Find the real part of zz.
Back to ProblemsView on AoPS