Ministry of Higher Education
and Scientifics research
University of Babylon
Complex Functions
Lecture 2
College of Education for Pure Sciences
Physics Department
Three Stage
Ali Hussein Mahmood Al-Obaidi
ali.alobaidi81@yahoo.com
1.3 Algebraic Properties:The following some properties of complex numbers
1. The commutative Law:-
2. The associative Law:-
3. The Distribution Law:4. Additive Identity :Since
, then
, we get
.
5. Multiplication Identity:Since
, then
, we get
6. Additive Inverse :-
For all
there exist
The complex number –
such that
is called additive Inverse element.
7. Multiplication Inverse:-
but we must make
by algebraic form .
1
.
Ministry of Higher Education
and Scientifics research
University of Babylon
Complex Functions
Lecture 2
College of Education for Pure Sciences
Physics Department
Three Stage
Ali Hussein Mahmood Al-Obaidi
ali.alobaidi81@yahoo.com
1.4 Complex Conjugate:The conjugate of complex number
is
.
 Complex Conjugate Properties:1.
2.
3.
4.
5. If
then is real number.
6. If
then is pure imaginary number.
7.
8.
9.
10. The conjugate operation satisfies (yield) distribution law in additive,
subtraction, multiplication, and division operation.
a.
b.
c.
d.
Remark:from
=
Ex:- Find
i.
2
Ministry of Higher Education
and Scientifics research
University of Babylon
Complex Functions
Lecture 2
Ali Hussein Mahmood Al-Obaidi
ii.
College of Education for Pure Sciences
Physics Department
Three Stage
ali.alobaidi81@yahoo.com
H.W
Sol:-
=
3