ZETA_in_olympiad wrote: $f$ 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 $m$? $\text{Re}(\frac 1{\overline z})=a$ $\iff$ $\frac x{x^2+y^2}=a$ $\iff$ $x^2+y^2\ne 0$ and $\left(x-\frac 1{2a}\right)^2+y^2=\frac 1{4a^2}$ And so the requested area is the area between circles : $C1$ : center $(4040,0)$ and radius $4040$ $C2$ : center $(4036,0)$ and radius $4036$ Hence solution $\boxed{m=4040^2-4036^2=32304}$

pco wrote: ...And so the requested area is the area between circles : $C1$ : center $(4040,0)$ and radius $4040$ $C2$ : center $(4036,0)$ and radius $4036$ Hence solution $\boxed{m=4040^2-4036^2=32304}$ Small computation error (thanks ucchash for PM) : ...And so the requested area is the area between circles : $C1$ : center $(1010,0)$ and radius $1010$ $C2$ : center $(1009,0)$ and radius $1009$ Hence solution $\boxed{m=1010^2-1009^2=2019}$