MathDB

SMT 2022 Algebra Tiebreaker #2

Source:

March 28, 2023

Problem Statement

What is the area of the region in the complex plane consisting of all points

z

satisfying both

|\tfrac{1}{z}-1|<1

and

|z-1|<1

? (

|z|

denotes the magnitude of a complex number, i.e.

|a+bi|=\sqrt{a^2+b^2}