MathDB

Let

z

be a complex number with

|z| = 2014

. Let

P

be the polygon in the complex plane whose vertices are

z

and every

w

such that

\tfrac{1}{z+w} = \tfrac{1}{z} + \tfrac{1}{w}

. Then the area enclosed by

P

can be written in the form

n\sqrt{3},

where

n

is an integer. Find the remainder when

n

is divided by

1000

Problem Statement