Complex number with a remainder... :O

Algebra Level 4

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 1/(z+w) = 1/z + 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.

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