preface

Prologue - The Beginning of Love

Chapter 1 Types of Numbers
1.
Types of numbers
2.
Quadratic equation root formula
3.
All quadratic equations can be solved by introducing the imaginary number i.
4.
Example of applying quadratic equations
5.
How to derive the root formula of a quadratic equation
6.
How to calculate square roots

Chapter 2 Expanding the imaginary number i to the complex number a＋bi
1.
Extension to complex numbers
2.
Properties of complex numbers (magnitude, angle) and the complex plane
3.
Arithmetic operations for complex numbers
4.
The four basic operations of complex numbers are plotted on the complex plane.
5.
What is a conjugate complex number?
6.
Practice problems

Chapter 3 Polar Coordinates
1.
Cartesian and polar coordinate systems
2.
Practice problems

Chapter 4: Euler's Formula Relating Exponential Functions to Complex Numbers
1.
Euler's formula
2.
Napier number (base of natural logarithms) e
3.
Euler's formula proof
4.
de Moivre's formula
5.
Polar Coordinates Teaching Using Exponents
6.
Definition of differentiation and differentiation of Napier numbers
7.
Practical examples of Napier numbers

Chapter 5: Euler's Formula and the Addition Theorem of Trigonometric Functions
1.
Addition theorem of trigonometric functions
2.
Derivation of the addition theorem for trigonometric functions
3.
Practice problems

Chapter 6: Properties of complex numbers, multiplication and division, and polar coordinate representation
1.
What is multiplication of complex numbers?
2.
What is division of complex numbers?
3.
Trigonometric table corresponding to the degree and radians systems
4.
Formula for exponent
5.
Logarithmic function
6.
(-1)×(-1)=1, meaning that debt×debt=savings

Chapter 7 Engineering Uses of Complex Numbers
1.
AC circuit
2.
Engineering Uses of Complex Numbers
3.
Effective value of household voltage
4.
Relative positional relationship of sine waves

supplement
Practice problems
References
Search

A guidebook that helps you understand everything from basic mathematics to electrical circuit theory!

Complex numbers are a very powerful calculation method when dealing with electrical circuits, especially AC circuits, and are used to calculate actual voltage and current waveforms.
Electrical circuit lectures in college are mainly about alternating current theory, and you must be able to treat voltage and current as complex numbers.
Also, in the qualification exam related to electricity, there are many problems that are solved using alternating current theory, that is, imaginary numbers and complex numbers.
This book is an introduction to imaginary and complex numbers, and helps readers understand the theory and calculations of electrical circuits using them. It also uses cartoons to explain essential information in a fun way.


■ Features and publisher reviews
1.
Learn imaginary and complex numbers easily through comics!!
This book uses comics to explain imaginary numbers, complex numbers, and even electrical theory in a fun way that readers can learn essential information.
In addition, the explanation was aimed at making it easy for beginners to understand imaginary numbers and complex numbers by thoroughly going over the basic concepts.

2.
The basics of electrical circuit studies!!
Since learning about imaginary and complex numbers is the foundation of electrical circuit studies, this book provides an understanding of electrical circuit calculations using complex numbers.

3.
Detailed calculation process!!
This book describes the calculation process in detail so that even readers with limited basic knowledge can easily understand it.