Ministry of Higher Education
and Scientifics research
University of Babylon
Complex Functions
Lecture 1
College of Education for Pure Sciences
Physics Department
Three Stage
Ali Hussein Mahmood Al-Obaidi
ali.alobaidi81@yahoo.com
1.1 Introduction :Natural numbers
also called positive integers and
denoted by . It were first used in counting. If and are natural
numbers, the sum
and product
,
or
are also
natural numbers. For this reason the set of natural numbers is said to
be closed under the operations of addition and multiplication or to
satisfy the closure property with respect to these operations.
Negative integers and zero, denoted by
respectively, are solutions of equations such as
where
and are any natural numbers. This leads to the operation of
subtraction, or inverse of addition, and we write
. The set
of positive and negative integers and zero is called the set of
integers, denoted by and is closed under the operation of addition,
multiplication and subtraction.
Rational numbers or fractions denoted by
such as
are solutions of equations such as
for all integers and
where
. This leads to operation of division or inverse of
multiplication, and we write
or
[called the aquatint
of and ] where is the numerator and is the denominator. The
set of rational numbers is closed under the operations of addition,
subtraction, multiplication and division, so long as division by zero is
excluded.
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Ministry of Higher Education
and Scientifics research
University of Babylon
Complex Functions
Lecture 1
Ali Hussein Mahmood Al-Obaidi
College of Education for Pure Sciences
Physics Department
Three Stage
ali.alobaidi81@yahoo.com
Irrational numbers such as
… and
are numbers which are not rational, i.e. cannot be expressed as
where and are integers and
.This numbers are solutions of
equations such as
where is positive irrational and isn't
complete square number.
The set of rational and irrational numbers is called the set of real
numbers denoted by . If we have the equation
and is
negative irrational and isn’t complete square number, then there is
no real number which is solution of equation. To solve this equation,
we defined a new numbers which called Imaginary numbers. From
this numbers, we get complex numbers set which is big set numbers
and denoted by . That is
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