Complex numbers
eBook - ePub

Complex numbers

  1. English
  2. ePUB (mobile friendly)
  3. Available on iOS & Android
eBook - ePub

Complex numbers

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

 

General form

The general form of a complex number,

image.png
is

image-1.png
where x and y are real numbers

image-2.png
and they are called the real part and the imaginary part of the complex number z, respectively. The imaginary unit

image-3.png
has the following property

image-4.png
The real and imaginary parts are denoted with

image-5.png
and

image-6.png
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

  1. Contents
  2. Introduction
  3. Part 1
  4. Theory
  5. General form
  6. Elementary operations
  7. Complex conjugate
  8. Modulus
  9. Graphical and vector representations
  10. Polar form
  11. Exponential form
  12. De Moivre's theorem
  13. Fundamental theorem of algebra
  14. Useful tips
  15. Part 2
  16. Exercises
  17. Text
  18. Solutions