Ministry of Higher Education
and Scientifics research
University of Babylon
Complex Functions
Lecture 7
College of Education for Pure Sciences
Physics Department
Three Stage
Ali Hussein Mahmood Al-Obaidi
ali.alobaidi81@yahoo.com
1.7 Polar Coordinates:If
number
is a point in the complex plan corresponding to the complex
or
, Then we see from fig. that
,
where
is called the modulus or absolute value of
of
[denoted by
],
is the angle which line
the positive
, and
, called the argument
make with
axis. That is
It follows that
θ
which is called the polar form of complex number, and
coordinates.
are called polar
For any complex number
, there corresponds only one value of
in
. However , any other interval of length
, for example
, can be used , is called the principal rang , and the value of
is called its principal value. The principal value denoted by
. So we
find
) where
.
The angle
may be obtained from the formula
.
1
, that is
Ministry of Higher Education
and Scientifics research
University of Babylon
Complex Functions
Lecture 7
College of Education for Pure Sciences
Physics Department
Three Stage
Ali Hussein Mahmood Al-Obaidi
ali.alobaidi81@yahoo.com
all
EX:-Express each of complex numbers in polar form .
i.
2
Ministry of Higher Education
and Scientifics research
University of Babylon
Complex Functions
Lecture 7
Ali Hussein Mahmood Al-Obaidi
ali.alobaidi81@yahoo.com
Thus
ii.
Thus
iii.
College of Education for Pure Sciences
Physics Department
Three Stage
H.W
3