Roots of a Complex Number
By: Junaid Mansuri
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This program was designed to find all n nth-roots of a complex number
which comes up in any introductory Complex Analysis course.

The syntax is: croot(z,n)
Where z is the complex number which can be in either polar form or 
rectangular form. And n is the degree of the root.
The set of roots is stored in the list named 'crt' and is displayed 
on the 'Prgm IO' screen.  The list can also be viewed from the 'Home'
screen by typing in 'crt' and pressing Enter.
Also, the output can be displayed in either polar form or rectangular 
form by simply changing the Mode under 'Complex Format'.


Example 1) Let's say we want to find the 4 4th-roots of 1.

	Namely, we want to find all complex numbers z such that
				z^4=1

	Simply type in on the prompt: croot(1,4)

The output on the 'Prgm IO' screen is {1, i, -1, -i}
This set of roots is stored as the list crt.


Example 2) Say we want to find all values of (-8i)^(1/3)

	Simply type in: croot(-8i,3)

The output on the 'Prgm IO' screen is {sqrt(3)-i, 2i, -sqrt(3)-i}
This set of roots is stored as the list crt.


Example 3) Finally suppose we want to find the 6 6th-roots of -1

	Simply type in: croot(-1,6)

As usual the set of roots is displayed on the 'Prgm IO' screen and
the set of roots is stored as the list crt.
When the 6 roots are displayed on the 'Prgm IO' screen, not all of
them are visible because the list is long.
In this case what one should do is simply go to the 'Home' screen,
type in crt and press Enter.
This way you can scroll through the entire list of roots.

____________________________________________________________________
Anyway, please enjoy the program.

If there are any problems, whatsoever, feel free to e-mail me at any 
time and I will be eager to assist you in any way I can.  If the
answer is incorrect for some reason please e-mail me the question so
that I can try to fix up the program.

Also, if you can think of ways that I can improve the program's speed
and accuracy, please e-mail me.

Sincerely,
Junaid Mansuri
jmansu1@uic.edu