An Investigation of Complex Numbers Using the Gauss-Lucas Theorem

Item

Title

An Investigation of Complex Numbers Using the Gauss-Lucas Theorem

Description

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.

Karen Stanish

Contributor

Keene State College

Creator

Alex S. Goss

Date

2017-10-11

Identifier

http://hdl.handle.net/20.500.12088/8109

Subject

Mathematics

Type

Presentation

Rights

http://rightsstatements.org/vocab/InC/1.0/

Item sets

AEC 2017 School of Sciences and Social Sciences

Site pages

School of Sciences and Social Sciences