Complex numbers E-Book

Alessio Mangoni

• Herausgeber: Dr. Alessio Mangoni
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Veröffentlichungsjahr: 2020

Beschreibung

This book is dedicated to complex numbers. In the first part we expose the theory, where the main arguments are: complex numbers in cartesian, polar and exponential forms, the complex conjugate, the modulus, properties and theorems about complex numbers, polynomial equations. In the second part we propose and solve some original exercise on the topics covered in the first part, to fix the concepts.

Leseprobe

Contents

Contents

Introduction

Part 1

Theory

General form

Elementary operations

Addition

Subtraction

Multiplication

Division

Complex conjugate

Properties

Useful relations

Modulus

Properties

Triangle inequality

Graphical and vector representations

Polar form

Exponential form

Euler's formula for trigonometry

Phase factors

Modulus of the exponential

De Moivre's theorem

Roots

Roots of unity

Fundamental theorem of algebra

Useful tips

Part 2

Exercises

Text

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

Exercise 6

Exercise 7

Exercise 8

Solutions

Exercise 1

Text

Solution

Exercise 2

Text

Solution

Exercise 3

Text

Solution

Exercise 4

Text

Solution

Exercise 5

Text

Solution

Exercise 6

Text

Solution

Exercise 7

Text

Solution

Exercise 8

Text

Solution

 

Elementary operations

Addition

Consider the two generic complex numbers in cartesian form



and