Complex numbers
eBook - ePub

Complex numbers

Alessio Mangoni

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eBook - ePub

Complex numbers

Alessio Mangoni

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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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Information

Year
2020
ISBN
9788835877646

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