MathDB

Complex numbers in geometry

Source: 2012 AIME I Problem 14

March 16, 2012

geometryalgebrapolynomialVietaanalytic geometrygraphing linesslope

Problem Statement

Complex numbers

a

b

and

c

are the zeros of a polynomial

P(z) = z^3+qz+r

, and

|a|^2+|b|^2+|c|^2=250

. The points corresponding to

a

b

, and

c

in the complex plane are the vertices of a right triangle with hypotenuse

h

. Find

h^2