Ministry of Higher Education
and Scientifics research
University of Babylon
Complex Functions
Lecture 9
College of Education for Pure Sciences
Physics Department
Three Stage
Ali Hussein Mahmood Al-Obaidi
ali.alobaidi81@yahoo.com
1.10 Extraction of Roots:The problem of extracting the
roots of a complex number is
that of solving the equation
for , when and positive integer
are given.
Let the polar form of be
where and
becomes
and Let
are as unknown. Then equation
where
Where
Thus
where
Let
then
1
Ministry of Higher Education
and Scientifics research
University of Babylon
Complex Functions
Lecture 9
College of Education for Pure Sciences
Physics Department
Three Stage
Ali Hussein Mahmood Al-Obaidi
ali.alobaidi81@yahoo.com
,
,
Thus
,
Example:a) Find the cube roots of
b) Find the square roots of
c) Find the cube roots of
SOL:a)
When
When
When
2
Ministry of Higher Education
and Scientifics research
University of Babylon
Complex Functions
Lecture 9
Ali Hussein Mahmood Al-Obaidi
College of Education for Pure Sciences
Physics Department
Three Stage
ali.alobaidi81@yahoo.com
Thus the roots is
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