Application of Complex Numbers to Prove Several Theorems in Plane Geometry

Geometry is a branch of mathematics that focuses on studying the characteristics of flat and spatial structures. One of the most well-known standard flat structures is the circle. Additionally, there are triangles formed by the intersection of three line segments. This study discusses the proofs of two theorems related to circles and triangles: the radius of the circumcircle of a triangle and Heron’s theorem. Heron’s theorem is used to determine the area of an arbitrary triangle. Unlike the conventional synthetic geometry approach, this article employs an alternative method, namely complex numbers, to prove these two central theorems.