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Find the area of a subset of a complex plane

Source: Bangladesh Mathematical Olympiad 2020 Problem 7

February 19, 2022

geometrycoordinate geometryalgebra

Problem Statement

f

is a function on the set of complex numbers such that

f(z)=1/(z*)

, where

z*

is the complex conjugate of

z

S

is the set of complex numbers

z

such that the real part of

f(z)

lies between

1/2020

and

1/2018

. If

S

is treated as a subset of the complex plane, the area of

S

can be expressed as

m× \pi

where

m

is an integer. What is the value of

m