2020 AMC 12A Problems/Problem 15
Problem
In the complex plane, let be the set of solutions to and let be the set of solutions to What is the greatest distance between a point of and a point of
Solution
Realize that will create an equilateral triangle on the complex plane with the first point at and two other points with equal magnitude at $1\pmi\sqrt{3}$ (Error compiling LaTeX. Unknown error_msg).
Also, realize that can be factored through grouping: will create points at and
Plotting the points and looking at the graph will make you realize that $1\pmi\sqrt{3}$ (Error compiling LaTeX. Unknown error_msg) and are the farthest apart and through Pythagorean Theorem, the answer is revealed to be ~lopkiloinm