Ministry of Higher Education
and Scientifics research
University of Babylon
Complex Functions
Lecture 5
College of Education for Pure Sciences
Physics Department
Three Stage
Ali Hussein Mahmood Al-Obaidi
ali.alobaidi81@yahoo.com
1.6 Geometric Representation of complex number:`
A complex number
can be considered as an ordered
pair (
), that is we can represent such numbers by points in an
plane called complex PLAN. Some time we refer to the and axes as
the real and imaginary axes respectively and the complex plan as the
plan.
(
)
O
A complex number
whose initial point is the origin
point (
) as in fig.
can be considered as a vector
and whose terminal (end) point is the
EX:- Graph each of the following:i.
ii.
iii.
H.W
Sol:-
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Ministry of Higher Education
and Scientifics research
University of Babylon
Complex Functions
Lecture 5
Ali Hussein Mahmood Al-Obaidi
College of Education for Pure Sciences
Physics Department
Three Stage
ali.alobaidi81@yahoo.com
According to the definition of the sum of two complex numbers,
corresponds to the point
. It also corresponds
to a vector with those coordinates as its components . Hence
is
represented by vector whose initial point is the origin and whose
terminal point is the point
as shown in fig.
O
The difference
is represented by vector from the point to
the point
. Addition of complex numbers corresponds to the
parallelogram low for addition of vectors. Thus to add the complex
numbers. and , we complete the parallelogram OABC . The diagonal
OB which pass in the origin corresponds to
, but the diagonal AC
which don’t pass in the origin corresponds to
.
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