#### Presentation Title

An Investigation of Complex Numbers Using the Gauss-Lucas Theorem

#### Presentation Type

Oral Presentation

#### School

School of Sciences and Social Sciences

#### Discipline

Mathematics

#### Mentor

Karen Stanish

#### Abstract

Have you ever wondered about the actual properties of complex numbers? Have you ever enjoyed or pondered at their computations and their geometric representation? This presentation will investigate some interesting properties of the complex numbers and their geometric representations. A complex number is a number of the form a+bi, where a and b are real numbers and i is the imaginary number such that when it is squared, it is equal to -1. These numbers are important and interesting because they allow us to extend the representation of numbers from one dimension into numbers in two dimensions, therefore we can represent complex numbers geometrically in the x-y-plane, which is a two-dimensional plane. After explaining and constructing the complex numbers, we will explore the Gauss-Lucas Theorem that makes clear the relationship between the roots of a complex polynomial and its derivative from calculus.

An Investigation of Complex Numbers Using the Gauss-Lucas Theorem

Have you ever wondered about the actual properties of complex numbers? Have you ever enjoyed or pondered at their computations and their geometric representation? This presentation will investigate some interesting properties of the complex numbers and their geometric representations. A complex number is a number of the form a+bi, where a and b are real numbers and i is the imaginary number such that when it is squared, it is equal to -1. These numbers are important and interesting because they allow us to extend the representation of numbers from one dimension into numbers in two dimensions, therefore we can represent complex numbers geometrically in the x-y-plane, which is a two-dimensional plane. After explaining and constructing the complex numbers, we will explore the Gauss-Lucas Theorem that makes clear the relationship between the roots of a complex polynomial and its derivative from calculus.