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Complex numbers
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About This Book
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.
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Yes, you can access Complex numbers by Alessio Mangoni in PDF and/or ePUB format, as well as other popular books in Mathematics & Complex Analysis. We have over one million books available in our catalogue for you to explore.
Information
Part 1
Theory
Ā
General form
The general form of a complex number,
ļæ¼
is
ļæ¼
where x and y are real numbers
ļæ¼
and they are called the real part and the imaginary part of the complex number z, respectively. The imaginary unit
ļæ¼
has the following property
ļæ¼
The real and imaginary parts are denoted with
ļæ¼
and
ļæ¼
The form of Eq. (1.1) is called the cartesian form of z, but there are also other forms to express a complex number, as we will see later.
If the imaginary part is null, y=0, the number z=x is real, while if the real part is null, x=0, the number z=iy is called a purely imaginary number.
Elementary operations
Addition
Consider the two generic complex numbers ...
Table of contents
- Contents
- Introduction
- Part 1
- Theory
- General form
- Elementary operations
- Complex conjugate
- Modulus
- Graphical and vector representations
- Polar form
- Exponential form
- De Moivre's theorem
- Fundamental theorem of algebra
- Useful tips
- Part 2
- Exercises
- Text
- Solutions